Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 2 - Nonlinear Functions - 2.2 Quadratic Functions; Translation and Reflection - 2.2 Exercises - Page 64: 1


Please see step-by-step for discussion.

Work Step by Step

The graph is a parabola which, if $a < 0$, opens down, and if $a > 0$, opens up. When $a \geq 1$, the graph is vertically stretched by factor a (each y-coordinate of $y=x^{2}$ increases by factor a), so the graph will be more narrow than the graph of $y=x^{2}$. (Narrow = the branches will be closer to the y-axis) When $0 \leq a \leq 1$, the graph of $y=x^{2}$ is vertically compressed, (each y-coordinate of $y=x^{2}$ decreases by factor a), so it becomes wider.
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