Answer
$$y= -\frac{1}{16}x^2 .$$
Work Step by Step
The focus is at $(0,-4)$ and the directrix is $y=4=-c$, hence $c=-4$. The parabola is vertical, opens downwards, and has the equation
$$y=\frac{1}{4c}x^2=-\frac{1}{16}x^2 .$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises - Page 636: 26
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