Answer
See graph below.
Work Step by Step
The question ONLY asks for a graph of the polar equation.
Given $r =-3 \cos 4θ$
Table of Values:
$(-3, 0)$
$(-3/2, \frac{\pi}{12})$
$(0, \frac{\pi}{8})$
$(3/2, \frac{2\pi}{12})$
$(3, \frac{\pi}{4})$
$(3/2, \frac{4\pi}{12})$
$(0, \frac{3\pi}{8})$
$(-3/2, \frac{5\pi}{12})$
Repeat the pattern until the angle goes back to $2\pi$
See graph below. It is in the shape of a flower/rose.
