Answer
$f$ can include $(-2,3)$
$a=\frac{3}{4}$
Work Step by Step
$(-2,3)$ is in second quadrant, so only the function $f$ could go through this point.
$$f(x)=ax^2$$
Substitute $x=-2$ and $f(x)=3$ to find $a$:
$$3=a(-2)^2$$
$$3=4a$$
$$a=\frac34$$