Answer
$${x^2} = \frac{9}{4}y$$
Work Step by Step
$$\eqalign{
& {\text{through the point }}\left( { - 3,4} \right),{\text{ opens up}} \cr
& {\text{The equation opens up}},{\text{ then the equation is of the form }} \cr
& {x^2} = 4py,\,\,\,p > 0 \cr
& {\text{We know the point }}\left( { - 3,4} \right) \cr
& {\left( { - 3} \right)^2} = 4p\left( 4 \right) \cr
& 9 = 16p \cr
& p = \frac{9}{{16}} \cr
& {\text{,then}} \cr
& {x^2} = 4\left( {\frac{9}{{16}}} \right)y \cr
& {x^2} = \frac{9}{4}y \cr} $$
