What muscles does the Barbell Banded Back Squat work?

Mainly the quads. It also works the glutes.

What equipment do you need for the Barbell Banded Back Squat?

It uses a barbell. Without it, the Dumbbell Squat and the Machine Goblet Sissy Squat train the same muscles the same way.

GymVim rates it intermediate. For a beginner-rated exercise on the same muscle and movement, see the Band Squat.

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A back squat with bands attached to the bar — adds resistance at the top of the rep where you're strongest.

Loop bands around the bar near the sleeves and anchor them to the bottom of the squat rack.
Step under the bar, position it on your upper traps, and unrack with feet shoulder-width apart.
Brace your core hard and squat down with control until your hip crease drops below your knees.
Drive explosively up through your heels, accelerating against the band tension as you stand.
Lock out at the top with hips fully extended, then reset your breath and brace before the next rep.
Complete 3 to 6 reps per set, prioritizing speed and bar control over pure load on the bar.

Letting the chest collapse forward at the bottom, turning the squat into a good-morning.
Slowing the ascent through the band tension instead of accelerating — defeats the point of accommodating resistance.
Setting up bands unevenly so the bar tilts during the lift, creating dangerous side-to-side load.
Using bands too heavy for the user's experience level, breaking form and risking the spine.

What muscles does the Barbell Banded Back Squat work?: Mainly the quads. It also works the glutes.
What equipment do you need for the Barbell Banded Back Squat?: It uses a barbell. Without it, the Dumbbell Squat and the Machine Goblet Sissy Squat train the same muscles the same way.
Is the Barbell Banded Back Squat good for beginners?: GymVim rates it intermediate. For a beginner-rated exercise on the same muscle and movement, see the Band Squat.