Answer
Vertex: $(2,-1)$
Foci: $(2,1)$
Directrix: $y=-2$
Axis of symmetry: $y$
Work Step by Step
The first thing we see is that the equation has the form:
$$(x-h)^2=4p(y-k)$$ where the vertex is $$(h,k)$$
This means the parabola opens up or down, and has axis of symmetry of $y$ and the directrix $y=-p$, so let's find $p$.
If we match the equations we find:
$(x-2)^2=8(y+1)$
$4p=8$
$p=\frac{8}{4}=2$
$h=-(-2)=2$
$k=-(1)=-1$
So the vertex is:
$(2,-1)$,
and the directrix:
$y=-p$
$y=-2$
In order to find the foci, we know that the foci is in the same axis as the vertex and is $p$ units away of it, so:
Foci $(h,k+p)$
Foci $(2,-1+2)$
Foci $(2,1)$
