Answer
$(x+2)^2=-16 (y-1)$
Work Step by Step
Because the vertex and the focus have the same $x$-coordinate it means that the parabola is vertical.
Since the focus is $1-(-3)=4$ units down from the vertex, it means that the parabola is facing down and $p=-4$.
The standard form of a vertical parabola is given as: $(x-h)^2=4p(y-k) ~~~(1)$
Here, we have $(h,k)=(-2,1)$, so $h=-2; k =1$.
Now, we will plug these values in equation (1) to obtain:
$(x-(-2))^2=4 (-4)(y-1) \implies (x+2)^2=-16 (y-1)$
