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Transformations Of Quadratic Functions

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Published in: Mathematics
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Transformations of Quadratic Functions

Wajiha M / Sharjah

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Qualification: Msc Statistics

Teaches: Economics, Mathematics, Sociology, Statistics

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  1. Lesson 9-3: Transformations of Quadratic Functions
  2. Transformation transformation changes the position or size of a figure • 3 types of transformations: 1. Translations 2. Dilations 3. 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 The graph of g(x) = ax2 is the graph of f(x) = x2 stretched or compressed vertically. If lal > 1, the graph off(x) = x2 is stretched vertically. If O < I al < 1, the graph of x2 is compressed vertically. lal > 1 O x
  5. Example 1: 2 Describe how the graph of x is related to the graph f(x) = u•nu f(x) d(x) 1 Answer: Since O < 1, the graph of f(x) —x2 is a 3 vertical compression of the graph y x 2
  6. Describe how the graph of Example 2: m(x) = + 1 is related to the graph f(x) = m(x) -2 Answer: Since 1 > O and 3 > 1, the graph of y + 1 is stretched vertically and then translated up 1 unit.
  7. Example 3: Describe how the graph of n(x) = is related to the graph of f(x) = A. n(x) is compressed vertically from f(x). B. n(x) is translated 2 units up from f(x). 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) -9<2 - 4 is related to the graph of f(x) A. D. b(x) is stretched vertically and translated 4 units down from f(x). b(x) is compressed vertically and translated 4 units down from f(x). b(x) is stretched horizontally and translated 4 units up from f(x). b(x) is stretched horizontally and translated 4 units down from f(x).
  9. Reflections The graph of —f(x) is the reflection of the graph of f(x) = x2 across the x-axis. The graph of f(—x) is the reflection of the graph of f(x) = x2 across the y-axis. (x) x —f(x)
  10. Example 1: How is the graph of related to the graph of f(x) = Three transformations are occurring: 1. 2. 3. 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.
  11. Answer: g(x) = + 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 7 is related to the graph of f (x) 10 x 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? unau A. D.
  14. Summary h, Horizontal Translation h units to the right if t) is positive I hl units to the left if his negative nana a, Reflection If a > O, the graph opens up. If a < O, the graph opens down. k, Vertical Translation k units up if kis posltive I kl units down if k is negative a, Dilation If I al > 1, the graph is stretched vertically. If O < I al < 1, the graph is compressed vertically. lal<l

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