Answer:
f(x) = -(1/4)(x - 2)^2 - 1
Step-by-step explanation:
Take any point (x,y) on the graph.
The distance of this point from the focus is equal to the distance of the point from the directrix.
So √ [(x - 2)^2 + (y + 2)^2 ] = y
(x - 2)^2 + (y + 2)^2 = y^2
(x - 2)^2 + y^2 + 4y + 4 = y^2
(x - 2)^2 + 4y + 4 = 0
4y = -(x - 2)^2 - 4
y = -(1/4)(x - 2)^2 - 1 (answer).
