Answer
$${\left( {y - 2} \right)^2} = - 12\left( {x - 1} \right)$$
Work Step by Step
$$\eqalign{
& {\text{vertex }}\left( {1,2} \right),\,\,{\text{directrix }}x = 4 \cr
& {\text{Because the directrix is }}x = - p + h \cr
& {\text{The equation is of the form }}{\left( {y - k} \right)^2} = 4p\left( {x - h} \right) \cr
& {\text{With vertex }}\left( {h,k} \right) \cr
& h = 1\,\,k = 2,\,\,\,\, \cr
& - p + h = 4 \cr
& - p + 1 = 4 \cr
& - p = 3 \cr
& p = - 3 \cr
& {\text{The equation is }} \cr
& {\left( {y - k} \right)^2} = 4p\left( {x - h} \right) \cr
& {\left( {y - 2} \right)^2} = 4\left( { - 3} \right)\left( {x - 1} \right) \cr
& {\left( {y - 2} \right)^2} = - 12\left( {x - 1} \right) \cr} $$
