Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = - 1.

f (x) = - 1/4 x^2

f (x) = 1/4 x^2

f (x) = - 4x^2

f (x) = 4x^2

Ok, so from previous question

(x-h) ^2=4p (y-k)

distance from focus to directix is 2

2/2=1=p

1>-1

focus is above the vertex

1 unit down from (0,1) is (0,0)

vertex at (0,0)

since focus is above, p is positive

(x-0) ^2=4 (1) (y-0)

x^2=4y

4y=x^2

divide both sides by 4

y = (1/4) x^2

f (x) = 1/4x^2

2nd one is answer