To add to that, if you find yourself failing in that way, off the top of my head there are some quick to somewhat quick fixes:
- keep your elbows under the bar.... that will brace everything from your lats up... but don't go too far and hyperextend or do a behind the neck clean grip (lol)
- squeeze your glutes on the way up... that will keep your hips from shooting back and up
- do more posterior chain work
- lower the weight
Quads are the main mover on back squats...