Answer
$(y-2)^2=12(x+1)$
Work Step by Step
1. As the vertex and focus has same y-coordinate, use equation $(y-k)^2=4p(x-h)$
2. The vertex $(-1,2)$ gives $h=-1, k=2$
3. The focus $(2,2)$ means $p+h=2$, thus $p=3$
4. We have the equation $(y-2)^2=12(x+1)$
