9-1 Graphing Quadratic Functions Algebra 1 Glencoe McGraw-Hill Linda Stamper and JoAnn Evans All graphs must be completed on graph paper – check out the LCMS website to download coordinate planes.
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9-1 Graphing Quadratic Functions
Algebra 1 Glencoe McGraw-Hill Linda Stamper and JoAnn Evans
All graphs must be completed on graph paper – check out the LCMS website to download coordinate planes.
0a where ,cbxaxy 2 A quadratic function is a function that can be written in the standard form:Every quadratic function has a U-shaped graph called a parabola.
Quadratic Functions
x
y
The parabola opens up if the value of a is positive.
x
y
The parabola opens down if the value of a is negative.
Will the parabola open up or down?
up
1x2x5y 2
down4x7x3y 2
down
4x2x7y 2
4x7x2y 2
Rewrite the equation in standard form first to determine the leading coefficient.
The vertex is the lowest point on parabolas that open up.The vertex is the highest point on parabolas that open down.
x
y
x
y
•
•
The lowest point is also known as the minimum.
The highest point is also known as the maximum.
axis (line) of
symmetry
axis (line) of
symmetry
The vertical line passing through the vertex that divides the parabola into two symmetric parts is called the axis (line) of symmetry.
x
y
x
y
•
•
axis (line) of
symmetry
axis (line) of
symmetry
Each point on the parabola that is on one side of the axis of symmetry has a corresponding point on the parabola on the other side of the axis. The vertex is the only point on the parabola that is on the axis of symmetry.
x
y
x
y
•
•
GRAPHING A QUADRATIC FUNCTION
1. Find the x-coordinate of the vertex, which is .a2
bx
2. Make a table of values. Using x-values, calculate at least two values to the left and two values to the right of the vertex. If all of your values are on one side of the vertex, you will graph half of a parabola.
3. Plot the points and connect them with a smooth curve to form a parabola. Put arrows on the ends of the parabola.
The axis of symmetry for y = ax2 + bx + c is the vertical
line.
a2b
x
The y-intercept of
y = ax2 + bx + c is the value
given for “c”.
Sketch the graph of .4x3xy 2 Find the x-coordinate of the vertex.
(Write formula for vertex, substitute the values and simplify.)
a2b
x
123
23Will the parabola
open up or down?
What is the value of “a”?
What is the value of “b”?
What is the y-intercept?
4x3xy 2 y,x
23
47
416
418
49
429
49
423
323
y2
47
,23
2
2464
4232y 2
2,2
3
4499
4333y 2
4,3
1
2431
4131y 2
2,1
0 intercept-y 4,0
x
x y
2
3
1
0
a2
b
y-intercept
-4
-2
-2
-4
4x3xy 2
23
47
matchy,
matchy!
x
y
•••
••
What is the equation for the
axis of symmetry?
23
x
x y
2
3
1
0
a2b
y-intercept
-4
-2
-2
-4
4x3xy 2
23
47
matchy,
matchy!
Copy the following on your graph paper - then graph.
.6xxy 2 Example 2
Example 3
Example 4
Example 5
3x2xy 2
1xy 2
8x6xy 2
Example 1
.5x2xy 2
Will the parabola open up or down?
What is the value of “a”?
What is the value of “b”?
What is the y-intercept?
Example 1 Sketch the graph of .5x2xy 2
a2b
x
122
22
1
5x2xy 2 y,x
1
6521
5121y 2
6,1
0 5020y 2 5,0
1
2521
5121y 2
2,1
2
5544
5222y 2
5,2
3
2569
5323y 2
2,3
x5x2xy 2
x y
-1
0
1
-2
-3
a2b
y-intercept
-6
-2
-5
-5
-2
matchy,
matchy!
x
y
••••
•x = –1
What is the equation for the axis of symmetry?
5x2xy 2
x y
-1
0
1
-2
-3
ab2
y-intercept
-6
-2
-5
-5
-2
matchy,
matchy!
Copy the following on your graph paper - then graph.
.6xxy 2 Example 2
Example 3
Example 4
Example 5
3x2xy 2
1xy 2
8x6xy 2
Example 1
.5x2xy 2
-1
0
1
2
Example 2 Sketch the graph of: .6xxy 2
x y
21
)12()1(
a2b
x
21
-4
-6
-6.25
-6
-4
matchy,
matchy!
4
25 x =
½
What is the equation for the axis of symmetry?
-1
0
1
2
3
Example 3 Sketch the graph of:
x y
0
-3
-4
-3
0
3x2xy 2
1)12()2(
a2b
x
matchy,
matchy!
x = 1
What is the equation for the axis of symmetry?
Example 4 Sketch the graph of:
-2
-1
0
1
2
x y
-3
0
1
0
-3
1xy 2
012
0a2
bx
match
y,match
y!
x = 0
What is the equation for the axis of symmetry?
Example 5 Sketch the graph of:
1
2
3
4
5
x y
3
0
-1
0
3
8x6xy 2
326
126
a2b
x
matchy,
matchy!
x = 3
What is the equation for the axis of symmetry?
ab
x2
9-A2 Page 475-477 #16–25,63-65.
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