Find the focus and directrix for each parabola below:

a)    y = -(1/8) ( x + 3)^2 - 2

The vertex is (-3, -2)

The parabola turns downward

In this form

(1/8) =   1/[4p]    so     p   =  2

The focus is    (-3, -2 - p)  =  (-3 , - 2 - 2)  =  (-3, -4)

The directrix  is  y  =  -2 + p  =  -2 + 2  = 0   

b )    4y = x^2 - 20

4y + 20  = x^2

4 ( y + 5) = (x - 0)^2

The vertex is  (0, -5)   and the parabola turns upward

In this form

4p = 4  ⇒  p = 1

The focus is   (0, -5 + p) =  ( 0, -5 + 1)   = (0, -4)

The directrix is

y =  -5 - p =  -5 - 1  = -6