Why would the front end shake badly when you put on the brakes?

Most likely you have warped rotors. If the rotors are warped, when you apply the brakes, the brake pads/caliper will be forced to follow the rotor and the vibriation will transmit via the steering wheel and brake pedal.

Answe

If the rotors are warped you will feel a pulsation or a bumping in the pedal when you step on it. It may also be a loose brake caliper. If you are getting a bad shaking I would definitely check the suspension components and the steering linkage for problems.