Appendix D - Graphing Techniques - Exercises - Page 449: 55

Refer to the curve in Black in Graph I

For $y = 2x^2 - 1,$ when $x = 2, y = 7;$ $x = 1, y = 1;$ $x = 0, y = -1;$ $x = -1, y = 1;$ $x = -2, y = 7$ As seen, $y = 2x^2 - 1$ is the vertical stretching of $y = x^2$ twice and then with a vertical translation of 1 unit down. Domain = $(−\infty, \infty)$ Range = $[-1, \infty)$