lesson 9-3: transformations of quadratic functions
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Lesson 9-3: Transformations of Quadratic Functions](https://reader036.vdocuments.net/reader036/viewer/2022081419/56813900550346895da0b93a/html5/thumbnails/1.jpg)
Lesson 9-3:Transformations of Quadratic Functions
![Page 2: Lesson 9-3: Transformations of Quadratic Functions](https://reader036.vdocuments.net/reader036/viewer/2022081419/56813900550346895da0b93a/html5/thumbnails/2.jpg)
Transformation
![Page 3: Lesson 9-3: Transformations of Quadratic Functions](https://reader036.vdocuments.net/reader036/viewer/2022081419/56813900550346895da0b93a/html5/thumbnails/3.jpg)
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
![Page 4: Lesson 9-3: Transformations of Quadratic Functions](https://reader036.vdocuments.net/reader036/viewer/2022081419/56813900550346895da0b93a/html5/thumbnails/4.jpg)
Dilations
![Page 5: Lesson 9-3: Transformations of Quadratic Functions](https://reader036.vdocuments.net/reader036/viewer/2022081419/56813900550346895da0b93a/html5/thumbnails/5.jpg)
Example 1: Describe how the graph of d(x) = x2 is related to the graph f(x) = x2.
__13
Answer: Since 0 < < 1, the graph
of f(x) = x2 is a vertical compression of
the graph y = x2.
__13
__13
![Page 6: Lesson 9-3: Transformations of Quadratic Functions](https://reader036.vdocuments.net/reader036/viewer/2022081419/56813900550346895da0b93a/html5/thumbnails/6.jpg)
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.
![Page 7: Lesson 9-3: Transformations of Quadratic Functions](https://reader036.vdocuments.net/reader036/viewer/2022081419/56813900550346895da0b93a/html5/thumbnails/7.jpg)
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.
![Page 8: Lesson 9-3: Transformations of Quadratic Functions](https://reader036.vdocuments.net/reader036/viewer/2022081419/56813900550346895da0b93a/html5/thumbnails/8.jpg)
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.
__12
![Page 9: Lesson 9-3: Transformations of Quadratic Functions](https://reader036.vdocuments.net/reader036/viewer/2022081419/56813900550346895da0b93a/html5/thumbnails/9.jpg)
Reflections
![Page 10: Lesson 9-3: Transformations of Quadratic Functions](https://reader036.vdocuments.net/reader036/viewer/2022081419/56813900550346895da0b93a/html5/thumbnails/10.jpg)
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.
![Page 11: Lesson 9-3: Transformations of Quadratic Functions](https://reader036.vdocuments.net/reader036/viewer/2022081419/56813900550346895da0b93a/html5/thumbnails/11.jpg)
Answer: g(x) = –3x2 + 1 is reflected across the x-axis, stretched by a factor of 3,
and translated up 1 unit.
![Page 12: Lesson 9-3: Transformations of Quadratic Functions](https://reader036.vdocuments.net/reader036/viewer/2022081419/56813900550346895da0b93a/html5/thumbnails/12.jpg)
Example 2: Describe how the graph of g(x) = x2 – 7 is related to the graph of f(x) = x2.
__15
Answer: (1/5) < 1, so the graph is vertically compressed and k = -7, so the graph is translated down 7 units
![Page 13: Lesson 9-3: Transformations of Quadratic Functions](https://reader036.vdocuments.net/reader036/viewer/2022081419/56813900550346895da0b93a/html5/thumbnails/13.jpg)
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?
![Page 14: Lesson 9-3: Transformations of Quadratic Functions](https://reader036.vdocuments.net/reader036/viewer/2022081419/56813900550346895da0b93a/html5/thumbnails/14.jpg)
Summary