Answer
See graph below.
Work Step by Step
The question ONLY asks for a graph of the polar equation.
Given $r^2 =\cos 2θ$
Table of Values:
$(1, 0)$
$(-1, 0)$
$(0, \frac{\pi}{4})$
$(0, \frac{3\pi}{4})$
See graph below. It is in the shape of a cardioid with a loop.