Answer
$x^2=-\frac{1}{4}(y-4)$
Work Step by Step
Vertex: $V(h,k)=V(0,4)$
$h=0$ and $k=4$
Equation of a parabola with vertical axis and vertex at $(h,k)$:
$(x-h)^2=4p(y-k)$
$x^2=4p(y-4)$
The parabola passes through the point $(1,0)$:
$1^2=4p(0-4)$
$1=-16p$
$p=-\frac{1}{16}$
Finally:
$x^2=4(-\frac{1}{16})(y-4)$
$x^2=-\frac{1}{4}(y-4)$
