Answer
$${\left( {y - 6} \right)^2} = 28\left( {x + 5} \right)$$
Work Step by Step
$$\eqalign{
& {\text{vertex }}\left( { - 5,6} \right),\,\,{\text{directrix }}x = - 12 \cr
& {\text{Because the directrix is }}x = - p + h \cr
& {\text{The equation is of the form }}{\left( {y - k} \right)^2} = 4p\left( {x - h} \right) \cr
& {\text{With vertex }}\left( {h,k} \right) \cr
& h = - 5,\,\,k = 6,\,\,\,\, \cr
& - p + h = - 12 \cr
& - p - 5 = - 12 \cr
& - p = - 7 \cr
& p = 7 \cr
& {\text{The equation is }} \cr
& {\left( {y - k} \right)^2} = 4p\left( {x - h} \right) \cr
& {\left( {y - 6} \right)^2} = 4\left( 7 \right)\left( {x + 5} \right) \cr
& {\left( {y - 6} \right)^2} = 28\left( {x + 5} \right) \cr} $$
