The standard form of equation of parabola is (x-h)^2=4p(y-k) where the directrix is y=k-p and the vertex is as point (h,k).
Thus given that the vertex is at (0,0)
y=k-p
the value of p will be:
-4=0-p
p=4
thus the equation will be:
(x-0)^2=4*4(y-0)
x^2=16y
hence;
y=1/16x^2
the answer is y=1/16x^2
