Algebra I Vocabulary Word Wall Cards Mathematics vocabulary word wall cards provide a display of mathematics content words and associated visual cues to assist in vocabulary development. The cards should be used as an instructional tool for teachers and then as a reference for all students. The cards are designed for print use only. Table of Contents Expressions and Operations Real Numbers Absolute Value Order of Operations Expression Variable Coefficient Term Scientific Notation Exponential Form Negative Exponent Zero Exponent Product of Powers Property Power of a Power Property Power of a Product Property Quotient of Powers Property Power of a Quotient Property Polynomial Degree of Polynomial Leading Coefficient Add Polynomials (group like terms) Add Polynomials (align like terms) Subtract Polynomials (group like terms) Subtract Polynomials (align like terms) Multiply Binomials Multiply Polynomials Multiply Binomials (model) Multiply Binomials (graphic organizer) Multiply Binomials (squaring a binomial) Multiply Binomials (sum and difference) Factors of a Monomial Factoring (greatest common factor) Factoring (by grouping) Factoring (perfect square trinomials) Virginia Department of Education 2018Algebra I Mathematics Vocabulary
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Algebra I Vocabulary Word Wall Cards
Mathematics vocabulary word wall cards provide a display of mathematics content words and associated visual cues to assist in vocabulary development The cards should be used as an instructional tool for teachers
and then as a reference for all students The cards are designed for print use only
Table of Contents
Expressions and OperationsReal NumbersAbsolute ValueOrder of OperationsExpressionVariableCoefficientTermScientific NotationExponential FormNegative ExponentZero ExponentProduct of Powers PropertyPower of a Power PropertyPower of a Product PropertyQuotient of Powers PropertyPower of a Quotient PropertyPolynomialDegree of PolynomialLeading CoefficientAdd Polynomials (group like terms)Add Polynomials (align like terms)Subtract Polynomials (group like terms)Subtract Polynomials (align like terms)Multiply BinomialsMultiply PolynomialsMultiply Binomials (model)Multiply Binomials (graphic organizer)Multiply Binomials (squaring a binomial)
Multiply Binomials (sum and difference)Factors of a MonomialFactoring (greatest common factor)Factoring (by grouping)Factoring (perfect square trinomials)Factoring (difference of squares)Difference of Squares (model)Divide Polynomials (monomial divisor)Divide Polynomials (binomial divisor)Square RootCube RootSimplify Numerical Expressions
Containing Square or Cube RootsAdd and Subtract Monomial Radical
ExpressionsProduct Property of RadicalsQuotient Property of Radicals
Equations and InequalitiesZero Product PropertySolutions or RootsZerosx-InterceptsCoordinate PlaneLiteral EquationVertical LineHorizontal LineQuadratic Equation (solve by factoring)Quadratic Equation (solve by graphing)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary
Quadratic Equation (number of real solutions)
InequalityGraph of an InequalityTransitive Property for InequalityAdditionSubtraction Property of
InequalityMultiplication Property of InequalityDivision Property of InequalityLinear Equation (standard form)Linear Equation (slope intercept form)Linear Equation (point-slope form)Equivalent Forms of a Linear EquationSlopeSlope FormulaSlopes of LinesPerpendicular LinesParallel LinesMathematical NotationSystem of Linear Equations (graphing)System of Linear Equations
(substitution)System of Linear Equations (elimination)System of Linear Equations (number of
solutions)Graphing Linear InequalitiesSystem of Linear InequalitiesDependent and Independent VariableDependent and Independent Variable
(application)Graph of a Quadratic EquationVertex of a Quadratic FunctionQuadratic Formula
FunctionsRelations (definition and examples)Function (definition)Functions (examples)DomainRangeFunction NotationParent Functions - Linear QuadraticTransformations of Parent Functions
StatisticsDirect VariationInverse VariationScatterplotPositive Linear RelationshipNegative Linear RelationshipNo Linear RelationshipCurve of Best Fit (linear)Curve of Best Fit (quadratic)Outlier Data (graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary
Real NumbersThe set of all rational and irrational
numbers
Natural Numbers 1 2 3 4 hellip
Whole Numbers 0 1 2 3 4 hellip
Integers hellip -3 -2 -1 0 1 2 3 hellip
Rational Numbers
the set of all numbers that can be written as the ratio of two integers
with a non-zero denominator (eg 23
5 -5 03 radic16 137 )
Irrational Numbersthe set of all nonrepeating nonterminating decimals
(eg radic7 π -23223222322223hellip)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 1
Absolute Value
|5| = 5 |-5| = 5
The distance between a numberand zero
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 2
5 units 5 units
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Order of Operations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 3
Grouping Symbols
Exponents an
MultiplicationDivision
Left to Right
AdditionSubtraction
Left to Right
( ) radic
|| [ ]
ExpressionA representation of a quantity that may contain numbers variables or
operation symbolsx
-radic26
34 + 2m
ax2 + bx + c
3(y + 39)2 ndash 89
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 4
Variable
2(y + radic3)
9 + x = 208
d = 7c - 5
A = r 2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 5
Coefficient
(-4) + 2x
-7y radic5
23 ab ndash 1
2
πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 6
Term3x + 2y ndash 8
3 terms
-5x2 ndash x
2 terms
23ab
1 term
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 7
Scientific Notationa x 10n
1 le |a | lt 10 and n is an integer
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 8
ExamplesStandard Notation Scientific Notation
17500000 175 x 107
-84623 -84623 x 104
00000026 26 x 10-6
-0080029 -80029 x 10-2
(43 x 105) (2 x 10-2) (43 x 2) (105 x 10-2) =86 x 105+(-2) = 86 x 103
66times106
2times103
662times 106
103 =33times106minus3=33times103
Exponential Form
an = a a a a∙ ∙ ∙ hellip a0
Examples
2 2 2 = 2∙ ∙ 3 = 8
n ∙ n ∙ n ∙ n = n4 3 3 3 x x = 3∙ ∙ ∙ ∙ 3x2 =
27x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 9
basen factors
exponent
Negative Exponent
a-n = 1an a 0
Examples
4-2 = 142 = 1
16
x4
y-2 = x4
1y2 = x4
1∙ y
2
1 = x4 y2
(2 ndash a)-2 = 1(2 ndash a )2 ane2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 10
Zero Exponenta0 = 1 a 0
Examples
(-5)0 = 1
(3x + 2)0 = 1
(x2y-5z8)0 = 1
4m0 = 4 1 = 4∙
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 11
Product of Powers Property
am ∙ an = am + n
Examples
x4 ∙ x2 = x4+2 = x6
a3 ∙ a = a3+1 = a4
w7 ∙ w-4 = w7 + (-4) = w3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 12
Power of a Power Property
(am)n = am middot n
Examples
(y4)2 = y4∙2 = y8
(g2)-3 = g2∙(-3) = g-6 = 1g6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 13
Power of a Product Property
(ab)m = am bm
Examples
(-3a4b)2 = (-3)2 (∙ a4)2∙b2 = 9a2b2
-1(2 x )3 = -1
23 ∙x3 = -18 x3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 14
Quotient of Powers Property
am
an = am ndash n a 0
Examples
x6
x5 = x6 ndash 5 = x1 = xy-3
y-5= y-3 ndash (-5 ) = y2
a4
a4 = a4-4 = a0 = 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 15
Power of Quotient Property
(ab )m= am
bm b0
Examples
(y3 )
4= y4
34 = y81
(5t )-3= 5-3
t-3 = 153
1t 3 = 1
53∙t3
1 = t3
53 = t3
125
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Polynomial
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 17
Example Name Terms7
6x monomial 1 term
3t ndash 112xy3 + 5x4y binomial 2 terms
2x2 + 3x ndash 7 trinomial 3 terms
Nonexample Reason
5mn ndash 8 variable exponent
n-3 + 9 negative exponent
Degree of a Polynomial
The largest exponent or the largest sum of exponents of a term within a
polynomial
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 18
Polynomial Degree of Each Term
Degree of Polynomial
-7m3n5 -7m3n5 rarr degree 8 8
2x + 3 2x rarr degree 13 rarr degree 0 1
6a3 + 3a2b3 ndash 216a3 rarr degree 3
3a2b3 rarr degree 5-21 rarr degree 0
5
Leading Coefficient
The coefficient of the first term of a polynomial written in descending
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
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f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Quadratic Equation (number of real solutions)
InequalityGraph of an InequalityTransitive Property for InequalityAdditionSubtraction Property of
InequalityMultiplication Property of InequalityDivision Property of InequalityLinear Equation (standard form)Linear Equation (slope intercept form)Linear Equation (point-slope form)Equivalent Forms of a Linear EquationSlopeSlope FormulaSlopes of LinesPerpendicular LinesParallel LinesMathematical NotationSystem of Linear Equations (graphing)System of Linear Equations
(substitution)System of Linear Equations (elimination)System of Linear Equations (number of
solutions)Graphing Linear InequalitiesSystem of Linear InequalitiesDependent and Independent VariableDependent and Independent Variable
(application)Graph of a Quadratic EquationVertex of a Quadratic FunctionQuadratic Formula
FunctionsRelations (definition and examples)Function (definition)Functions (examples)DomainRangeFunction NotationParent Functions - Linear QuadraticTransformations of Parent Functions
StatisticsDirect VariationInverse VariationScatterplotPositive Linear RelationshipNegative Linear RelationshipNo Linear RelationshipCurve of Best Fit (linear)Curve of Best Fit (quadratic)Outlier Data (graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary
Real NumbersThe set of all rational and irrational
numbers
Natural Numbers 1 2 3 4 hellip
Whole Numbers 0 1 2 3 4 hellip
Integers hellip -3 -2 -1 0 1 2 3 hellip
Rational Numbers
the set of all numbers that can be written as the ratio of two integers
with a non-zero denominator (eg 23
5 -5 03 radic16 137 )
Irrational Numbersthe set of all nonrepeating nonterminating decimals
(eg radic7 π -23223222322223hellip)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 1
Absolute Value
|5| = 5 |-5| = 5
The distance between a numberand zero
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 2
5 units 5 units
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Order of Operations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 3
Grouping Symbols
Exponents an
MultiplicationDivision
Left to Right
AdditionSubtraction
Left to Right
( ) radic
|| [ ]
ExpressionA representation of a quantity that may contain numbers variables or
operation symbolsx
-radic26
34 + 2m
ax2 + bx + c
3(y + 39)2 ndash 89
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 4
Variable
2(y + radic3)
9 + x = 208
d = 7c - 5
A = r 2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 5
Coefficient
(-4) + 2x
-7y radic5
23 ab ndash 1
2
πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 6
Term3x + 2y ndash 8
3 terms
-5x2 ndash x
2 terms
23ab
1 term
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 7
Scientific Notationa x 10n
1 le |a | lt 10 and n is an integer
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 8
ExamplesStandard Notation Scientific Notation
17500000 175 x 107
-84623 -84623 x 104
00000026 26 x 10-6
-0080029 -80029 x 10-2
(43 x 105) (2 x 10-2) (43 x 2) (105 x 10-2) =86 x 105+(-2) = 86 x 103
66times106
2times103
662times 106
103 =33times106minus3=33times103
Exponential Form
an = a a a a∙ ∙ ∙ hellip a0
Examples
2 2 2 = 2∙ ∙ 3 = 8
n ∙ n ∙ n ∙ n = n4 3 3 3 x x = 3∙ ∙ ∙ ∙ 3x2 =
27x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 9
basen factors
exponent
Negative Exponent
a-n = 1an a 0
Examples
4-2 = 142 = 1
16
x4
y-2 = x4
1y2 = x4
1∙ y
2
1 = x4 y2
(2 ndash a)-2 = 1(2 ndash a )2 ane2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 10
Zero Exponenta0 = 1 a 0
Examples
(-5)0 = 1
(3x + 2)0 = 1
(x2y-5z8)0 = 1
4m0 = 4 1 = 4∙
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 11
Product of Powers Property
am ∙ an = am + n
Examples
x4 ∙ x2 = x4+2 = x6
a3 ∙ a = a3+1 = a4
w7 ∙ w-4 = w7 + (-4) = w3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 12
Power of a Power Property
(am)n = am middot n
Examples
(y4)2 = y4∙2 = y8
(g2)-3 = g2∙(-3) = g-6 = 1g6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 13
Power of a Product Property
(ab)m = am bm
Examples
(-3a4b)2 = (-3)2 (∙ a4)2∙b2 = 9a2b2
-1(2 x )3 = -1
23 ∙x3 = -18 x3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 14
Quotient of Powers Property
am
an = am ndash n a 0
Examples
x6
x5 = x6 ndash 5 = x1 = xy-3
y-5= y-3 ndash (-5 ) = y2
a4
a4 = a4-4 = a0 = 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 15
Power of Quotient Property
(ab )m= am
bm b0
Examples
(y3 )
4= y4
34 = y81
(5t )-3= 5-3
t-3 = 153
1t 3 = 1
53∙t3
1 = t3
53 = t3
125
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 16
Polynomial
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 17
Example Name Terms7
6x monomial 1 term
3t ndash 112xy3 + 5x4y binomial 2 terms
2x2 + 3x ndash 7 trinomial 3 terms
Nonexample Reason
5mn ndash 8 variable exponent
n-3 + 9 negative exponent
Degree of a Polynomial
The largest exponent or the largest sum of exponents of a term within a
polynomial
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 18
Polynomial Degree of Each Term
Degree of Polynomial
-7m3n5 -7m3n5 rarr degree 8 8
2x + 3 2x rarr degree 13 rarr degree 0 1
6a3 + 3a2b3 ndash 216a3 rarr degree 3
3a2b3 rarr degree 5-21 rarr degree 0
5
Leading Coefficient
The coefficient of the first term of a polynomial written in descending
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 42
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Quotient Propertyof Radicals
The nth root of a quotient equals the quotient of the nth roots of the numerator
and denominatornradic ab= nradica
nradicb
a ge 0 and b ˃ 0
Example
radic5y2 = radic5
radicy2 = radic5y y ne 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 43
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Zero Product Property
If ab = 0then a = 0 or b = 0
Example(x + 3)(x ndash 4) = 0
(x + 3) = 0 or (x ndash 4) = 0x = -3 or x = 4
The solutions or roots of the polynomial equation are -3 and 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 44
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Solutions or Rootsx2 + 2x = 3
Solve using the zero product property
x2 + 2x ndash 3 = 0(x + 3)(x ndash 1) = 0
x + 3 = 0 or x ndash 1 = 0x = -3 or x = 1
The solutions or roots of the polynomial equation are -3 and 1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 45
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Zeros The zeros of a function f(x) are the values of
x where the function is equal to zero
The zeros of a function are also the solutions or roots of the related equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 46
f(x) = x2 + 2x ndash 3Find f(x) = 0
0 = x2 + 2x ndash 30 = (x + 3)(x ndash 1)
x = -3 or x = 1
The zeros of the function f(x) = x2 + 2x ndash 3 are -3 and 1 and are located at the
x-intercepts (-30) and (10)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
x-InterceptsThe x-intercepts of a graph are located where the graph crosses the x-axis and
where f(x) = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 47
f(x) = x2 + 2x ndash 3
0 = (x + 3)(x ndash 1)0 = x + 3 or 0 = x ndash 1
x = -3 or x = 1
The zeros are -3 and 1The x-intercepts are
-3 or (-30) and 1 or (10)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Coordinate Plane
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 48
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Literal EquationA formula or equation that consists
primarily of variables
Examples
Ax + By = C
A = 12
bh
V = lwh
F = 95 C + 32
A = πr2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 49
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Vertical Line
x = a (where a can be any real number)
Example x = -4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 50
-5 -4 -3 -2 -1 0 1 2 3
-4
-3
-2
-1
0
1
2
3
4
Vertical lines have undefined slope
y
x
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Horizontal Line
y = c(where c can be any real number)
Example y = 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 51
-4 -3 -2 -1 0 1 2 3 4
-2
-1
0
1
2
3
4
5
6
7
Horizontal lines have a slope of 0
x
y
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Quadratic Equation(Solve by Factoring)
ax2 + bx + c = 0 a 0
Example solved by factoring
Solutions to the equation are 2 and 4 Solutions are 2 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 52
x2 ndash 6x + 8 = 0 Quadratic equation
(x ndash 2)(x ndash 4) = 0 Factor
(x ndash 2) = 0 or (x ndash 4) = 0 Set factors equal to 0
x = 2 or x = 4 Solve for x
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Quadratic Equation(Solve by Graphing)
ax2 + bx + c = 0a 0
Example solved by graphing
x2 ndash 6x + 8 = 0
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 53
Solutions to the equation are the x-coordinates2 4 of the points where the function crosses the x-axis
Graph the related function
f(x) = x2 ndash 6x + 8
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Quadratic Equation(NumberType of Real Solutions)
ax2 + bx + c = 0 a 0
Examples Graph of the related function
Number and Type of SolutionsRoots
x2 ndash x = 32 distinct Real
roots(crosses x-axis twice)
x2 + 16 = 8x
1 distinct Real root with a
multiplicity of two (double root)(touches x-axis but
does not cross)
12x2 ndash 2x + 3 = 0 0 Real roots
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 54
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
InequalityAn algebraic sentence comparing two
quantities
Symbol Meaning
lt less than less than or equal to greater than greater than or equal to not equal to
Examples -105 ˃ -99 ndash 12
8 lt 3t + 2
x ndash 5y ge -12
x le -11
r 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 55
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Graph of an Inequality
Symbol Example Graph
lt x lt 3
-3 y
t -2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 56
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Transitive Property of Inequality
If Thena b and b c a ca b and b c a c
Examples If 4x 2y and 2y 16
then 4x 16
If x y ndash 1 and y ndash 1 3 then x 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 57
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
AdditionSubtraction Property of Inequality
If Thena gt b a + c gt b + ca b a + c b + ca lt b a + c lt b + ca b a + c b + c
Exampled ndash 19 -87
d ndash 19 + 19 -87 + 19d -68
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 58
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Multiplication Property of Inequality
If Case Then a lt b c gt 0 positive ac lt bca gt b c gt 0 positive ac gt bca lt b c lt 0 negative ac gt bca gt b c lt 0 negative ac lt bc
Example If c = -25 gt -3
5(-2) lt -3(-2)
-10 lt 6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 59
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Division Property of Inequality
If Case Then
a lt b c gt 0 positive ac lt b
c
a gt b c gt 0 positive ac gt b
c
a lt b c lt 0 negative ac gt b
c
a gt b c lt 0 negative ac lt b
c
Example If c = -4-90 -4t
-90-4 -4 t
-4
225 t
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 60
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Linear Equation
(Standard Form)Ax + By = C
(A B and C are integers A and B cannot both equal zero)
Example
-2x + y = -3
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 61
-3 -2 -1 0 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
x
y
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Linear Equation (Slope-Intercept Form)
y = mx + b(slope is m and y-intercept is b)
Example y = - 43 x + 5
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 62
3
-4
(05)m = -4
3
b = 5
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Linear Equation (Point-Slope Form)
y ndash y1 = m(x ndash x1)where m is the slope and (x1y1) is the point
Example Write an equation for the line that passes through the point (-41) and has a slope of 2
y ndash 1 = 2(x ndash (-4))y ndash 1 = 2(x + 4)
y = 2x + 9
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 63
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Equivalent Forms of a Linear Equation
Forms of a Linear Equation
Example 3 y=6 ndash 4 x
Slope-Intercepty = mx + b
y=minus43x+2
Point-Slopey ndash y1 = m(x ndash x1)
yminus (minus2 )=minus43
( xminus3)
StandardAx + By= C
4 x+3 y=6
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 64
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
SlopeA number that represents the rate of change
in y for a unit change in x
The slope indicates the steepness of a line
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 65
2
3
Slope = 23
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Slope Formula The ratio of vertical change to
horizontal change
slope = m =
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 66
y
x
y2 ndash y1
x2 ndash x1
(x2 y2)
(x1 y1)
B
A
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Slopes of Lines
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 67
Line phas a positive slope
Line n has a negative
slope
Vertical line s has an undefined slope
Horizontal line t has a zero slope
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Perpendicular LinesLines that intersect to form a right angle
Perpendicular lines (not parallel to either of the axes) have slopes whose product is -1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 68
Example The slope of line n = -2 The slope of line p = 1
2 -2 ∙ 1
2 = -1 therefore n is perpendicular to p
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Parallel LinesLines in the same plane that do not intersect
are parallelParallel lines have the same slopes
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 69
Example The slope of line a = -2 The slope of line b = -2
-2 = -2 therefore a is parallel to b
ab
x
y
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
Mathematical Notation
EquationInequality Set Notation
x=minus5 minus5
x=5orx=minus34 5 minus34
ygt 83 y ∶ ygt 8
3
xle234 xorx le234
Empty (null) set empty
All Real Numbers x ∶ x All Real Numbers
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 70
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
System of Linear Equations
(Graphing)-x + 2y = 32x + y = 4
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 71
The solution (1 2) is the
only ordered pair that
satisfies both equations (the point of intersection)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
System of Linear Equations (Substitution)
x + 4y = 17y = x ndash 2
Substitute x ndash 2 for y in the first equation
x + 4(x ndash 2) = 17
x = 5
Now substitute 5 for x in the second equation
y = 5 ndash 2
y = 3
The solution to the linear system is (5 3)
the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 72
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
System of Linear Equations (Elimination)
-5x ndash 6y = 85x + 2y = 4
Add or subtract the equations to eliminate one variable -5x ndash 6y = 8+ 5x + 2y = 4
-4y = 12 y = -3
Now substitute -3 for y in either original equation to find the value of x the eliminated variable
-5x ndash 6(-3) = 8 x = 2
The solution to the linear system is (2-3) the ordered pair that satisfies both equations
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 73
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
System of Linear Equations
(Number of Solutions)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 74
Number of Solutions
Slopes and y-intercepts
Graph
One solution Different slopes
No solutionSame slope and
different -intercepts
Infinitely many
solutions
Same slope andsame y-
interceptsx
y
x
y
x
y
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 95
Examplesf(x) = xt(x) = -xh(x) = -3xd(x) = -1
3x
y
x
Quadratic Function(Transformational Graphing)
Vertical Translationh(x) = x2 + c
Vertical translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 96
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
Examplesf(x) = x2
g(x) = x2 + 2t(x) = x2 ndash 3
y
x
Quadratic Function(Transformational Graphing)
Vertical Dilation (agt0)h(x) = ax2
Vertical dilation (stretch or compression) of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 97
-5 -4 -3 -2 -1 0 1 2 3 4 5
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = 2x2
t(x) = 13x2
y
x
Quadratic Function(Transformational Graphing)
Vertical DilationReflection (alt0)h(x) = ax2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 98
-5 -4 -3 -2 -1 0 1 2 3 4 5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Examples f(x) = x2
g(x) = -2x2
t(x) = -13 x2
y
x
Quadratic Function(Transformational Graphing)
Horizontal Translation
h(x) = (x + c)2
Horizontal translation of f(x) = x2
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 99
Examplesf(x) = x2
g(x) = (x + 2)2
t(x) = (x ndash 3)2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-1
0
1
2
3
4
5
6
7
8
9y
x
Multiple Representations of
Functions
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 100
Words
y equals one-half x minus 2
Equationy=1
2xminus2
Tablex y
-2 -30 -22 -14 0
Graph
Direct Variationy = kx or k = y
x
constant of variation k 0
Example y = 3x or 3 = y
x
3 = minus6minus2
=minus3minus1
=31=6
2
The graph of all points describing a direct variation is a line passing through the
origin
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 101
x
y
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x y-2 -6-1 -30 01 32 6
Inverse Variation
y = kx or k = xy
constant of variation k 0 Example
y = 3x or xy = 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 102
y
x
The graph of all points describing an inverse variation relationship are two curves that
are reflections of each other
ScatterplotGraphical representation of the
relationship between two numerical sets of data
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 103
y
x
Positive Linear Relationship (Correlation)
In general a relationship where the dependent (y) values increase as independent values (x) increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 104
y
x
Negative Linear Relationship (Correlation)In general a relationship where the
dependent (y) values decrease as independent (x) values increase
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 105
y
x
No Linear Relationship (Correlation)
No relationship between the dependent (y) values and independent (x) values
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 106
y
x
Curve of Best Fit(Linear)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 107
Equation of Curve of Best Fity = 11731x + 19385
Curve of Best Fit(Quadratic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 108
Equation of Curve of Best Fity = -001x2 + 07x + 6
Outlier Data(Graphic)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 109
x
y
-2
-6
-1
-3
0
0
1
3
2
6
Absolute Value
Order of Operations
Expression
Variable
Coefficient
Term
Scientific Notation
Exponential Form
Negative Exponent
Zero Exponent
Product of Powers Property
Power of a Power Property
Power of a Product Property
= =
Power of Quotient Property
Polynomial
Degree of a Polynomial
Leading Coefficient
Add Polynomials
Add Polynomials
3g3 + 6g2 ndash g ndash 7
Subtract Polynomials
Multiply Binomials
Multiply Polynomials
Multiply Binomials
Multiply Binomials
Multiply Binomials
(Sum and Difference)
Factors of a Monomial
Factoring
(Greatest Common Factor)
Factoring
(By Grouping)
Example
Factoring
(Perfect Square Trinomials)
Factoring
(Difference of Squares)
Difference of Squares (Model)
Divide Polynomials
Divide Polynomials (Binomial Divisor)
Square Root
Cube Root
Simplify Numerical Expressions Containing
Add and Subtract Monomial Radical Expressions
Product Property of Radicals
Quotient Property
Zero Product Property
Solutions or Roots
Zeros
x-Intercepts
Coordinate Plane
Literal Equation
A = πr2
Quadratic Equation
Quadratic Equation
Inequality
Graph of an Inequality
Transitive Property of Inequality
AdditionSubtraction Property of Inequality
d -68
Division Property of Inequality
225 t
The graph of the linear equation is a straight line and represents all solutions (x y) of the equation
Linear Equation (Slope-Intercept Form)
Linear Equation (Point-Slope Form)
Equivalent Forms of a Linear Equation
Slope
Slope Formula
Slopes of Lines
Perpendicular Lines
Parallel Lines
Mathematical Notation
(Graphing)
System of Linear Equations
(Substitution)
System of Linear Equations
(Elimination)
System of Linear Equations
(Number of Solutions)
Graphing Linear Inequalities
System of Linear Inequalities
Dependent and
Independent Variable
Dependent and
Independent Variable
Graph of a Quadratic Equation
Relation
Function
Functions
Function Notation
Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Transformations of Parent Functions
Linear Function
Linear Function
Vertical dilation (stretch or compression) of the parent function f(x) = x
Vertical dilation (stretch or compression) with a reflection of f(x) = x
Vertical translation of f(x) = x2
Vertical dilation (stretch or compression) of f(x) = x2
Vertical dilation (stretch or compression) with a reflection of f(x) = x2
Multiple Representations of Functions
Direct Variation
Inverse
Variation
Scatterplot
Positive Linear Relationship (Correlation)
Negative Linear Relationship (Correlation)
No Linear Relationship (Correlation)
Curve of Best Fit
Curve of Best Fit
Outlier Data
(Graphic)
x
x
Graphing Linear Inequalities
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 75
The graph of the solution of a linear inequality is a half-plane bounded by the graph of its related linear equation Points on the boundary are included unless the inequality contains only lt or gt
-6-5-4-3-2-1 0 1 2 3 4-5-3-113579
1113
Example Graph
y x + 2
y gt -x ndash 1
y
y
x
System of Linear Inequalities
Solve by graphingy x ndash 3y -2x + 3
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 76
The solution region contains all ordered pairs that are solutions to both inequalities in the system
(-11) is one of the solutions to the system located in the solution
region
y
Example
y = 2x + 7
Dependent andIndependent Variable
x independent variable(input values or domain set)
y dependent variable(output values or range set)
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 77
Dependent andIndependent Variable
(Application)
Determine the distance a car will travel going 55 mph
d = 55h
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 78
independent dependenth d0 01 552 1103 165
Graph of a Quadratic Equation
y = ax2 + bx + ca 0
Example y = x2 + 2x ndash 3
The graph of the quadratic equation is a curve (parabola) with one line of symmetry and one vertex
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 79
-6 -5 -4 -3 -2 -1 0 1 2 3 4
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13y
x
line of symmetry
vertex
Vertex of a Quadratic Function
For a given quadratic y = ax2+ bx + c the vertex (h k) is found by computing
h =minusb2a and then evaluating y at h to find k
Example y=x2+2 xminus8
h=minusb2a
= minus22(1)
=minus1
k=(minus1 )2+2 (minus1 )minus8
k=minus9
The vertex is (-1-9)
Line of symmetry is x=hx=minus1
Virginia Department of Education 2018 Algebra I Mathematics Vocabulary ndash Card 80
Quadratic Formula Used to find the solutions to any quadratic