How do I find the focus and diretrix for y = x^2 -4

The parabola is centered at (0,-4) so:

x^2 = y + 4

In this case 4p = 1 so p = 1/4

Therefore, the focus is at (0, -4 +1/4) = (0, -15/4)
The directrix is just : -4 -1/4 = -17/4

F(0,-3 3/4)

y=-4 1/4