By : Ana Cristina Andrade

Quadratics Journal

By: Ana Cristina Andrade

What is a Quadratic function?A Quadratic function is a function that has the form y=ax²+bx+c. When it is graphed it is a parabola. The parabola can be upright or upsidedown depending on the sing of “a”. It can also be wider or skiner depending on the absolute value of “a”

WHAT IS A QUADRATIC FUNCTION?

QUADRATIC AND LINEAR FUNCTIONS:

Quadratic functions Linear function

Standard form: Y=ax²+bx+cVertex form: y=a(x-h) ²+kWhen it is graph it is a parabola

One variable solved for xWhen it is graph it is a lineSlope= rise/run -> y₁-y₂/x₁-x₂Slope intercept form: y=mx+bPoint slope form: y-y₁ = m (x-x₁)

Examples:

Quadratics:Linear:

1. Y= 3x²+2x-7

2.Y= 7x²-9x-8

3.Y=-2x²+10x-5

1. Y= 2x-72.Y= 9x-83.Y=-10x-5

Graphing quadratic functions:To graph quadric functions you use : y=a(x-b) ²+c

C: Moves vertex up or down C unitspositive goes upNegative goes down

B:Moves vertex left or right B unitsPositive – leftNegative - right

A:Less than 0 – Goes down (like a rainbow)More than 0- Goes up (like a horse shoe).Greater than 1 – skinierLess than 1 - wider

Less than 0

More than 0

MAXIMUM AND MINIMUMWhen the parabola opens up, it has a minimum value at the vertex and when it opens down it has a maximum value at the vertex.

Parabola

EXAMPLES:

Solving quadratic equations By graphing

STEPS:1. GRAPH THE FUNCTION• IDENTIFY A, B AND C• CALCULATE BY USING –B/(2 A) BY

PLUGGING IN THE NUMBERS.• USE T-TABLE TO GRAPH

2. FIND X-INTERCEPT(S) ON THE GRAPH3. YOUR SOLUTIONS ARE THE X-

INTERCEPTS.

EXAMPLES:

Solving quadratic equations By square roots

1.Leave X² alone2.Find the square root of the numbers3.If the one of the numbers or the

number has no exact square root, then factor the number and find the square root of one or both of thoes numbers.

4.Then write pluss minus infront the number.

EXAMPLES:

Solving quadratic equations using factoring:

STEPS:1.WRITE THE EQUATION IN STANDARD FORM2.FIND GCF3.CANCEL GRATEST COMMON FACTOR BY

DIVIDING THAT NUMBER ON BOTH SIDES4.FACTOR THE TRINOMIAL5.EQUAL EACH FACTOR TO 06.SOLVE EACH LINEAR EQUATION

Examples:

SOLVING QUADRATIC EQUATIONSUSING COMPLETING THE SQUARE:Steps:1.The coeficient of X² must be =12.Isolate C3.Complete the square4.Add (b/2)² to both sides5.Write as a binomial squared.6.Solve by using square root both sides7.Dont forget the +- (pluss minus)8.Isolate the variable

Examples:

SOLVING QUADRATICS USINGTHE QUADRATIC FORMULA:

Steps:1. Write in standard

form your equation.

2.Find a, b, c3.Plug them in the

formula4.solve

The Quadratic Formula:

Discriminant in the quadraticformula

To solve a quadratic eqation we can first calculate the discriminant to determine number of solutions. If the discriminant is positive, the equation has two solutions. If it is 0 it has one solution. If it is negative, then the equation has no real solution.

Examples: