Answer
$${x^2} = - 8\left( {y - 2} \right)$$
Work Step by Step
$$\eqalign{
& {\text{From the graph we got the following data:}} \cr
& {\text{Directrix }}y = 4,\,\,\,\,{\text{vertex}}\left( {0,2} \right) \cr
& {\text{The axis of symmetry is }}y,{\text{ then the equation of the parabola is}} \cr
& {\text{of the form}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\left( {x - h} \right)^2} = 4p\left( {y - k} \right) \cr
& {\text{vertex }}\left( {h,k} \right) \cr
& {\text{directrix }}y = - p + k \cr
& \cr
& {\text{then,}} \cr
& {\text{vertex}}\left( {0,2} \right) \cr
& {\text{vertex }}\left( {h,k} \right) \Rightarrow \,\,\,\,\,h = 0,\,\,\,\,k = 2 \cr
& {\text{directrix }}y = - p + k \Rightarrow \,\, - p + 2 = 4 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,p = - 2 \cr
& \cr
& {\text{An equation of the parabola is }}{\left( {x - h} \right)^2} = 4p\left( {y - k} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\left( {x - 0} \right)^2} = 4\left( { - 2} \right)\left( {y - 2} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{x^2} = - 8\left( {y - 2} \right) \cr} $$
