9-1 Graphing Quadratic Functions

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


-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



-2

-1

0

1

2

x y

-3

0

1

0

-3

1xy 2

012

0a2

bx

match

y,match

y!

x = 0



1

2

3

4

5

x y

3

0

-1

0

3

8x6xy 2

326

126

a2b

x

matchy,

matchy!

x = 3


ab

x2

9-A2 Page 475-477 #16–25,63-65.

Documents

9-1 Graphing Quadratic Functions