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Chapter 9 11 Glencoe Geometry Study Guide and Intervention Translations 9-2 Draw Translations A translation is a transformation that moves all points

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9-2 Study Guide and Intervention Measuring Angles and Arcs Angles and Arcs A central angle is an angle whose vertex is at the center of a circle and whose

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9-2 Study Guide and Intervention (continued) Translations Translations In The Coordinate Plane A vector can be used to translate a figure

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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

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Study Guide and Intervention (continued) Points Lines and Planes 9 AB and CD 10 XY and YZ X Y Z 3x 5 5x 1 9x 2

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480 ?? Glencoe Geometry Page 4 NAME DATE PERIOD 9-2 Study Guide and Intervention Translations Translations Using Coordinates A transformation called a

[PDF] Solutions reflections and trans handoutpdf

9-1 Practice Reflections Draw the image of each figure under a reflection in line 2 NAME AC No It's a reflection of Figure 1 It's a translation

[PDF] 3-19-14 - periodo 93 homework 93 (571314 21-23 31)

19 mar 2014 · 9-2 NAME_Brady Rochen _DATE 3-18-14 PERIOD O Study Guide and Intervention Translations Translations Using Coordinates A transformation

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10-9 Study Guide and Intervention Translations A translation is the movement of a Triangle ABC has vertices A(-4 -2) B(-2 0) and C(?1 ?3)

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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

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)

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

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

6. g(x) = -

1 2 + x 2

Translation of Translation of f(x) = x

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) 2 Translation of Translation of Translation of f x ) = x 2 f x ) = x 2 up 8 9 unit. f(x) = x 2 down 0.3 unit. to the left 4 units. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Chapter 9 18 Glencoe Algebra 1

Dilations and Reflections A dilation is a transformation that makes the graph narrower or wider than the parent graph. A reflection flips a figure over the x - or y -axis.

The graph of

f x ) = ax 2 stretches or compresses the graph of f x ) = x 2

If |a| > 1, the graph of f(x) = x

2 is stretched vertically. If 0 |a| < 1, the graph of f(x) = x 2 is compressed vertically.

The graph of the function

f x ) ? ips the graph of f x ) = x 2 across the x -axis.

The graph of the function

f x ) ? ips the graph of f x ) = x 2 across the y -axis. Describe how the graph of each function is related to the graph of f x ) = x 2

9-3Study Guide and Intervention (continued)

Transformations of Quadratic Functions

0 < a < 1

a = 1 a > 1 xy O f x x 2 f x x 2

Example

a. g(x) = 2x 2

The function can be written as

f x ) = ax 2 where a = 2. Because |a| > 1, the graph of y = 2x 2 is the graph of y = x 2 that is stretched vertically.b. g(x) = - 1 2 x 2 - 3

The negative sign causes a reflection

across the x -axis. Then a dilation occurs in which a 1 2 and a translation in which k = -3. So the graph of g(x) = - 1 2 x 2 - 3 is reflected across the x -axis, dilated wider than the graph of f x ) = x 2 , and translated down 3 units.

Exercises

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

1. g(x) = -5x

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

3. g(x) = -

1 4 x 2 - 1

Compression of Translation of f(x) = x

Dilation of

f x ) = x 2 f x ) = x 2 narrower than to the left 1 unit and wider than the graph of the graph of f x ) = x 2 re? ected over the x-axis. f(x) = x 2 re? ected over re? ected over the the x-axis translated x -axis. down 1 unit. xy O f x x 2 f x 2 x 2 xf(x) g(x)y Oquotesdbs_dbs8.pdfusesText_14

[PDF] [PDF] 9-3 - Study Guide and Intervention - PBS Math 8

NAME DATE PERIOD

Lesson 9-3

Chapter 9 17 Glencoe Algebra 1

The graph of

2 vertically.

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

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

The graph of

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

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

Transformations of Quadratic Functions

Example

The value of

0. Therefore,

The value of

3, and

3 < 0. Thus, the

Exercises

1. g(x) = x

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

Translation of Translation of

Translation of f(x

4. g(x) = 20 + x

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

6. g(x) = -

Translation of Translation of f(x) = x

Translation of

7. g(x) = x

8. g(x) = x

NAME DATE PERIOD

Chapter 9 18 Glencoe Algebra 1

The graph of

If |a| > 1, the graph of f(x) = x

The graph of the function

The graph of the function

9-3Study Guide and Intervention (continued)

Transformations of Quadratic Functions

0 < a < 1

Example

The function can be written as

The negative sign causes a reflection

Exercises

1. g(x) = -5x

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

3. g(x) = -

Compression of Translation of f(x) = x

Dilation of