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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Lesson 9-3

Chapter 9 17 Glencoe Algebra 1

9-3 Translations A translation is a change in the position of a figure either up, down, left, right, or diagonal. Adding or subtracting constants in the equations of functions translates the graphs of the functions.

The graph of

g x ) = x 2 k translates the graph of f x ) = x

2 vertically.

If k > 0, the graph of f(x) = x

2 is translated k units up.

If k < 0, the graph of f(x) = x

2 is translated k | units down.

The graph of

g x ) = (x - h) 2 is the graph of f(x) = x 2 translated horizontally.

If h > 0, the graph of f(x) = x

2 is translated h units to the right.

If h < 0, the graph of f(x) = x

2 is translated | h | units to the left.Study Guide and Intervention

Transformations of Quadratic Functions

Describe how the graph of each function is related to the graph of f x ) = x 2

Example

a. g(x) = x 2 + 4

The value of

k is 4, and 4

0. Therefore,

the graph of g x ) = x 2 + 4 is a translation of the graph of f x ) = x 2 up 4 units. g(x) f x x b. g(x) = (x + 3) 2

The value of

h is

3, and

3 < 0. Thus, the

graph of g x ) = (x + 3) 2 is a translation of the graph of f x ) = x 2 to the left 3 units. y x O f(x) g x

Exercises

Describe how the graph of each function is related to the graph of f(x) = x 2

1. g(x) = x

2 + 1 2. g(x) = (x - 6) 2

3. g(x) = (x + 1)

2

Translation of Translation of

f x ) = x 2

Translation of f(x

) = x2 f x ) = x 2 up 1 unit. to the right 6 units. to the left 1 unit.

4. g(x) = 20 + x

2

5. g(x) = (-2 + x)

2

6. g(x) = -

1 2 + x 2

Translation of Translation of f(x) = x

2

Translation of

f x ) = x 2 up 20 units. to the right 2 units. f(x) = x 2 down 1 2 unit.

7. g(x) = x

2 8 9

8. g(x) = x

2 - 0.3 9. g(x) = (x + 4)quotesdbs_dbs2.pdfusesText_3