Answer
The equation of parabola is $(x -2)^2 = 2(y +2)$ which has focus $(2,-\frac{3}{2})$ and directrix is: $x=-\frac{5}{2}$.
Work Step by Step
The equation of a upward parabola is:
$(x -h)^2 = 4p(y - k)$.
Also, the equation of downward parabola is :
$(y -h)^2 = 4p(x - k)$.
Vertex: $(h, k) or (k,h)$
Focus: $(h, k + p) or (k+p,h)$.
As we are given that vertex: $(2,-2)$
so, $p=\frac{1}{2}$
Hence, the equation of parabola is $(x -2)^2 = 2(y +2)$ which has focus $(2,-\frac{3}{2})$ and directrix is: $x=-\frac{5}{2}$.
