Answer
$${\left( {x - 4} \right)^2} = 8\left( {y - 3} \right)$$
Work Step by Step
$$\eqalign{
& {\text{vertex }}\left( {4,3} \right),\,\,{\text{focus }}\left( {4,5} \right) \cr
& {\text{Because the focus is upward the vertex}} \cr
& {\text{The equation is of the form }}{\left( {x - h} \right)^2} = 4p\left( {y - k} \right) \cr
& {\text{With vertex }}\left( {h,k} \right){\text{ and focus }}\left( {h,p + k} \right) \cr
& h = 4,\,\,k = 3,\,\,\,\,p + 3 = 5,\,\,\,p = 2 \cr
& \cr
& {\text{The equation is }} \cr
& {\left( {x - h} \right)^2} = 4p\left( {y - k} \right) \cr
& {\left( {x - 4} \right)^2} = 4\left( 2 \right)\left( {y - 3} \right) \cr
& {\left( {x - 4} \right)^2} = 8\left( {y - 3} \right) \cr} $$
