The function y = ax²: practice problems

For the function $y = -\frac{3}{2}x^2$, answer the following.

1. (1)Find $y$ when $x = -4$.
2. (2)Find all values of $x$ with $y = -24$.

For $y = ax^2$, the rate of change as $x$ goes from $-1$ to $3$ is $6$. Find $a$.

The graph of $y = 2x^2$ and a line meet at A and B, whose $x$-coordinates are $-2$ and $2$. Find the area of $\triangle \mathrm{OAB}$, where O is the origin.

The graph of $y = ax^2$ passes through $(1,\ 2)$. Find $a$.

For $y = 4x^2$ with $-3 \leqq x \leqq -2$, find the range of $y$.

The graph of $y = \frac{1}{4}x^2$ meets line AB at A and B, with $x$-coordinates $-6$ and $6$. Point P (not O) on the positive $y$-axis makes the area of $\triangle \mathrm{PAB}$ equal to that of $\triangle \mathrm{OAB}$. Find P.