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McGraw Hill Integrated II, 2012 View details

5. Solving Quadratic Equations by Using the Quadratic Formula

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Exercise 66 Page 139

Rewrite the function g(x) in terms of f(x).

Compress vertically by a factor of 12.

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We see that the function g(x) is half the function f(x). 2x^2= 1/2* 4x^2 ⇔ g(x)= 1/2 * f(x) Considering the table of possible transformations, the graph of g(x) is the graph of f(x) compressed vertically by a factor of 12. It is a compression since 0 < | 12 |< 1.

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Possible Transformations

The following table illustrates the general form for all possible transformations of functions.

Transformations of f(x)
Vertical Translations	Translation up k units, k>0 y=f(x)+ k
Vertical Translations	Translation down k units, k<0 y=f(x)+ k
Horizontal Translations	Translation right h units, h>0 y=f(x- h)
Horizontal Translations	Translation left h units, h<0 y=f(x- h)
Vertical Stretch or Compression	Vertical stretch, a>1 y= af(x)
Vertical Stretch or Compression	Vertical compression, 0< a< 1 y= af(x)
Horizontal Stretch or Compression	Horizontal stretch, 0< b<1 y=f( bx)
Horizontal Stretch or Compression	Horizontal compression, b>1 y=f( bx)
Reflections	In the x-axis y=- f(x)
Reflections	In the y-axis y=f(- x)

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Exercises p.137-139

Exercise 66 Page 139

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