No. The focus is 2 below the vertex. Therefore p = -2
Your first equation is correct, and properly locates the vertex. I have no idea how you came up with the next two.
(x+1)^2 = -8 (y-2)
Find an equation of the parabola.
vertex:(-1,2) focus:(-1,0)
(x+1)^2 = 4p(y-2)
(x+1)^2 = 0(y-2)
(x+1)^2 = (y-2)
Am I correct?
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