#### Answer

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.