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