NAME DATE PERIOD Lesson 8 Reteach

NAME _____________________________________________ DATE __________________ PERIOD _________

Lesson 8 Reteach

Quadratic Functions

A quadratic function, such as A = s2, is a function in which the greatest power of the variable is 2. Its graph is U-shaped, opening upward or downward.

Example 1 Graph y = -2x2.

x

-2x2

y

-2

-2(2)2 = -8 -8

-1

-2(-1)2 = -2 -2

0

-2(0)2 = 0

0

1

-2(1)2 = -2

-2

2

-2(2)2 = -8

-8

(x, y) (-2, -8) (-1, -2)

(0, 0) (1, -2) (2, -8)

y

0

x

y = -2x 2

Example 2 Graph y = x2 - 3.

x

x2 - 3

y

-2

(-2)2 -3 = 1

1

-1

(-1)2 -3 = -2 -2

0

(0)2 -3 = -3 -3

1

(1)2 -3 = -2 -2

2

(2)2 -3 = 1

1

(x, y) (-2, 1) (-1, -2) (0, -3) (1, -2) (2, 1)

y

O

x

y = x2 -3

Exercises Graph each function.

1. y = 2x2

y

2. y = -0.5x2

y

O

x

3. y = x2 - 1

y

Copyright ? The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.

O

x

4. y = 2x2 + 4

y

5. y = -x2 - 3

y

O

x

6. y = -3x2 + 1

y

O

x

Course 3 ? Chapter 4 Functions

O

x

O

x

69

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