Write the equation of a parabola with the focus of (-2,4) and directrix y=2. Show your work including a sketch.

If the focus  is   ( -2 , 4)   and the directrix  is y = 2, the vertex  is ( -2, 3)

So....p  = 1      and we have the form

4p(y - 3) =   ( x + 2)^2

4(y - 3)  =   (x + 2)^2

y - 3  =  (1/4)(x + 2)^2

y = (1/4) ( x + 2)^2 +  3