Answer
$${y^2} = \frac{4}{3}x$$
Work Step by Step
$$\eqalign{
& {\text{The parabola is symmetric with respect to the }}x{\text{ - axis, then }} \cr
& {\text{the equation is of the form }}{y^2} = 4px \cr
& {\text{The point }}\left( {3,2} \right){\text{ is on the graph, it must satisfy the equation}}{\text{.}} \cr
& {y^2} = 4px \cr
& {\left( 2 \right)^2} = 4p\left( 3 \right) \cr
& 4 = 4p\left( 3 \right) \cr
& p = \frac{1}{3} \cr
& {\text{Then, the equation is:}} \cr
& {y^2} = 4\left( {\frac{1}{3}} \right)x \cr
& {y^2} = \frac{4}{3}x \cr} $$
