## Calculus 8th Edition

The equation of parabola is $(x -2)^2 = 2(y +2)$ which has focus $(2,-\frac{3}{2})$ and directrix is: $x=-\frac{5}{2}$.
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: $x=-\frac{5}{2}$.