Answer
$(x+1)^2=4(y-2)$
Work Step by Step
We are given the parabola:
Vertex: $(-1,2)$
Focus: $(-1,3)$
As the focus and the vertex have the same $x$-coordinate, the parabola is vertical. Its standard equation is:
$(x-h)^2=4p(y-k)$
Determine $h,k$ using the vertex:
$(h,k)=(-1,2)$
$h=-1$
$k=2$
Determine $p$ using the focus:
$(h,k+p)=(-1,3)$
$k+p=3$
$2+p=3$
$p=1$
The parabola's equation is:
$(x+1)^2=4(1)(y-2)$
$(x+1)^2=4(y-2)$
