1 / 14

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.

hannah-golden
Download Presentation

Lesson 9-3: Transformations of Quadratic Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related