# Appendix D - Graphing Techniques - Exercises - Page 449: 57

Refer to the curve in Black in Graph I

#### Work Step by Step

For $f(x) = 2(x - 2)^2 - 4,$ when $x = 4, y = 4;$ $x = 3, y = -2;$ $x = 2, y = -4;$ $x = 1, y = -2;$ $x = 0, y = 4$ As seen, $f(x) = 2(x - 2)^2 - 4$ is the horizontal translation to the right by 2 units, the vertical stretching twice and the vertical translation down by 4 units of $f(x) = x^2$. Domain = $(−\infty, \infty)$ Range = $[-4, \infty)$

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