Answer
Quadrant I
Work Step by Step
$\frac{-7\pi}{4}$ radians
It is a negative angle and obtained by rotating the terminal side clockwise $\frac{7\pi}{4}$ = $2\pi$ - $\frac{\pi}{4}$ radians.
We use |$\frac{-7\pi}{4}$| or $\frac{7\pi}{4}$ to determine the rotation.
So $\frac{-7\pi}{4}$ radians lies in quadrant I.
Find the attachment.