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Lesson 9-3: Transformations of Quadratic Functions

Lesson 9-3: Transformations of Quadratic Functions. Transformation. A transformation changes the position or size of a figure 3 types of transformations: Translations Dilations Reflections. Vocabulary.

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Lesson 9-3: Transformations of Quadratic Functions

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  1. Lesson 9-3:Transformations of Quadratic Functions

  2. Transformation • A transformationchanges the position or size of a figure • 3 types of transformations: • Translations • Dilations • Reflections

  3. 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.

  4. Dilations

  5. Example 1: Describe how the graph of d(x) = x2is related to the graph f(x) = x2. 1 __ 3 1 1 __ __ 3 3 Answer: Since 0 < < 1, the graph of f(x) = x2 is a vertical compression of the graph y = x2.

  6. 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.

  7. 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).

  8. Example 4: Describe how the graph of b(x) = x2 – 4 is related to the graph of f(x) = x2. 1 __ 2 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).

  9. Reflections

  10. 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 dilationoccurs, where a= 3. • Last, a translationoccurs, where h= 1.

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

  12. Example 2: Describe how the graph of g(x) = x2 – 7 is related to the graph of f(x) = x2. 1 __ 5 Answer: (1/5) < 1, so the graph is vertically compressed and k = -7, so the graph is translated down 7 units

  13. 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

  14. Summary

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