Thank you for posting the figure. Without it, I would have thought the parabola has a vertical axis.
For a parabola with a horizontal axis (as in this case), the equation of the parabola is
f(y)=a(y-k)^2+h
where (h,k) is the vertex.
Substituting (h,k)=(2,-4),
f(y)=a(y+4)^2+2...................(1)
as the equation of the parabola, with the value of "a" yet unknown.
Since we are given that the parabola passes through the point (-3,-3), we can substitute the corresponding x,y values in (1) to solve for a.
f(y)=-3=a(-3+4)^2+2
solve for a
a=(-3-2)/(1^2)=-5
So the equation of the parabola is f(y)=-5(y+4)^2+2