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

Since  the vertex is halfway between the focus and the directrix, the vertex must be at (-2,3)

So....the distance between the vertex and the focus  =  1  = p

So.....using   4py  =  (x - h)^2 + k       where p = 1, h = -2  and k = 3

And we have

4(1)y  = (x - -2)^2 + 3

4y  = ( x + 2) ^2   + 3          multiply both sides by (1/4)

y =  (1/4) ( x + 2)^2  + 3

Here's the graph : https://www.desmos.com/calculator/dfundaxw40