Lesson 9-3:Transformations of Quadratic Functions

Transformation

A dilation is a transformation that makes the graph narrower or wider than the parent graph.

A reflection flips a figure over the x-axis or y-axis.

Vocabulary

Dilations

Example 1: Describe how the graph of d(x) = x2 is related to the graph f(x) = x2.

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Answer: Since 0 < < 1, the graph

of f(x) = x2 is a vertical compression of

the graph y = x2.

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Example 2: Describe how the graph of m(x) = 2x2 + 1 is related to the graph f(x) = x2.

Answer: Since 1 > 0 and 3 > 1, the graph of y = 2x2 + 1 is stretched vertically and then translated up 1 unit.

A. n(x) is compressed vertically from f(x).

B. n(x) is translated 2 units up from f(x).

C. n(x) is stretched vertically from f(x).

D. n(x) is stretched horizontally from f(x).

Example 3: Describe how the graph of n(x) = 2x2 is related to the graph of f(x) = x2.

A. b(x) is stretched vertically and translated 4 units down from f(x).

B. b(x) is compressed vertically and translated 4 units down from f(x).

C. b(x) is stretched horizontally and translated 4 units up from f(x).

D. b(x) is stretched horizontally and translated 4 units down from f(x).

Example 4: Describe how the graph of b(x) = x2 – 4 is related to the graph of f(x) = x2.

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Reflections

Example 1: How is the graph of g(x) = –3x2 + 1

related to the graph of f(x) = x2 ?

Three transformations are occurring:

1.First, the negative sign causes a reflection across the x-axis.

2.Then a dilation occurs, where a = 3.

3.Last, a translation occurs, where h = 1.

Answer: g(x) = –3x2 + 1 is reflected across the x-axis, stretched by a factor of 3,

and translated up 1 unit.

Example 2: Describe how the graph of g(x) = x2 – 7 is related to the graph of f(x) = x2.

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Answer: (1/5) < 1, so the graph is vertically compressed and k = -7, so the graph is translated down 7 units

A. y = –2x2 – 3

B. y = 2x2 + 3

C. y = –2x2 + 3

D. y = 2x2 – 3

Example 2: Which is an equation for the function shown in the graph?

Summary