a) When $a$ and $a^2$ are both positive. b) When $a < -1$ and $a>1$
Work Step by Step
a) If $a$ is negative, then $a^2$ is positive. Thus, the graphs won't be in the same quadrants. If $a$ is positive, then $a^2$ is also positive (and would be in the same quadrants. b) Graphs with smaller absolute values of coefficients have wider graphs. $a > a^2$ when $0 < a < 1$. However, a graph can also open down and still be wider than another graph. So, $a < a^2$ when $-1 < a < 0$ (and the graph of $a$ will be narrower than $a^2$.