## Calculus with Applications (10th Edition)

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.