## Calculus (3rd Edition)

$$y= \frac{1}{16}x^2 .$$
The focus is at $(0,4)$ and the directrix is $y=-4=-c$, hence $c=2$. The parabola is vertical, opens upwards, and has the equation $$y=\frac{1}{4c}x^2=\frac{1}{16}x^2 .$$