There is no greater crime in the gym than cutting your squat high. The squat is used to build power throughout the entire lower body, abs and back. By cutting your depth short you are cheating yourself of strength and hypertrophy gains, putting your lower back at risk, and making yourself look like an idiot.
The acceptable depth for a squat is lowering yourself until your hips break parallel with your knees. This depth will give you three white lights in the great sport of powerlifting and still allow you to use a tremendous amount of weight.
For the most hypertrophy gains and to develop mobility, ass to grass squats are the key. You will have to swallow your pride and use a little less weight, but the added range of motion will create more stress on your muscles.
Also, always remember to keep your chest up, look up or ahead, push the knees out and the ass back.
When I see someone squat down and intentionally cut their depth I pretty much feel they should lose their rights to use the squat rack. It is really a sign of mental weakness.
Shame on the high squatters I say!
Think about it, if you aren't sure if you can squat the weight through the full range of motion then you should recruit a spotter or put some safety racks just below your intended depth. Basically, make it safe to fail so you can squat like you mean it.
I dump the weight into the rack several times a week. It's no big deal, I just call it a negative rep and move on to the next drill.
Bottom line, swallow your pride, drop the weight, and squat to full depth.
This is a real squat!
I will give you one caveat, quarter squats do have their place in the gym. I find them usefull for strength athletes trying to get used to heavier weights. Simply squat until you hit your max weight, then add about 50lbs and do a few reps of quarter squats. This will build confidence and upper back strength. Or you can just do what I do and set up the safety rack so you do a full negative squat into the rack.
Speaking of squatting into the rack, here is the training session I did today to build strength and muscle.
joint circles, bar hanging
empty barbell complex
A1 Safety Squat Cambered Bar Squats, ass to grass
95 x 5, 135 x 5, 185 x 5, 225 x 5, 275 x 5, 315 x 3, 365 x 1, 405 x 1, 455 x miss
This bar is a little bigger so it might actuall weight more but whatever
I put a belt on at 405lbs
A2 Fat Bar/Axle Clean and Press
95 x 5, 135 x 5, 185 x 3, 215 x 3, 235 x 1, 1, 215 x 3, 3,