Answer
$${\left( {y - 2} \right)^2} = 3\left( {x + 3} \right)$$
Work Step by Step
$$\eqalign{
& {\text{parabola with vertex at }}\left( { - 3,2} \right){\text{ and }}y{\text{ - intercepts }}\left( {0,5} \right){\text{and }}\left( {0, - 1} \right) \cr
& {\text{The parabola intercepts the }}y{\text{ - axis into two points, then}} \cr
& {\text{The equation of the parabola is of the form }}{\left( {y - k} \right)^2} = 4p\left( {x - h} \right) \cr
& \cr
& {\text{Vertex }}\left( {h,k} \right):\left( { - 3,2} \right),\,\,\,\,\,h = - 3,\,\,k = 2 \cr
& {\left( {y - 2} \right)^2} = 4p\left( {x + 3} \right) \cr
& {\text{We know the point }}\left( {0,5} \right) \cr
& {\left( {5 - 2} \right)^2} = 4p\left( {0 + 3} \right) \cr
& {\text{Solve for }}p \cr
& 9 = 4p\left( 3 \right) \cr
& p = \frac{3}{4} \cr
& \cr
& {\text{The equation of the parabola is}} \cr
& {\left( {y - 2} \right)^2} = 4\left( {\frac{3}{4}} \right)\left( {x + 3} \right) \cr
& {\left( {y - 2} \right)^2} = 3\left( {x + 3} \right) \cr} $$
