Lesson 9-3: Transformations of Quadratic Functions

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Lesson 9-3Transformations of Quadratic
Functions
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Transformation

• A transformation changes the position or size of
  a figure
• 3 types of transformations
• Translations
• Dilations
• Reflections

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Vocabulary

• 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.

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Dilations
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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 gt 0 and 3 gt 1, the graph of y
2x2 1 is stretched vertically and then
translated up 1 unit.
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Example 3 Describe how the graph of n(x) 2x2
is related to the graph of f(x) x2.
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).
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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).
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Reflections
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Example 1 How is the graph of g(x) 3x2 1
related to the graph of f(x) x2 ?

• Three transformations are occurring
• First, the negative sign causes a reflection
  across the x-axis.
• Then a dilation occurs, where a 3.
• Last, a translation occurs, where h 1.

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Answer g(x) 3x2 1 is reflected across the
x-axis, stretched by a factor of 3, and
translated up 1 unit.
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Answer (1/5) lt 1, so the graph is vertically
compressed and k -7, so the graph is
translated down 7 units
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Example 2 Which is an equation for the function
shown in the graph?
A. y 2x2 3 B. y 2x2 3 C. y 2x2
3 D. y 2x2 3
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Summary