we have
Parabola
with vertex (0,0) and focus (0,-4)
we know that
is a vertical parabola that opens down
the standard form of the equation is of the form
(x-h)²=-4p(y-k)
where
(h,k) is the vertex----------> (0,0)
p is the distance from the vertex to the focus or directrix
in this problem
p=4
(x-h)²=-4p(y-k)------> x²=-16y-------> y=-(1/16)x²
the answer is the option
D.)y = negative one divided by sixteen x2
see the attached figure
