My car shakes in the front end when I feather the gas. what causes this?

You haven't said what make and model of car it is.

On a rear wheel drive car a worn universal joint in the driveshaft (propshaft) can cause the symptoms you describe. It's sometimes referred to as a 'yoke'.

Wear causes the universal joint/propshaft to be out of line/balance and causes the vibration when the car is moving. Another symptom is a 'clunk' when the car engages gear. That clunk noise is also caused by wear.

You can check it quite easily. get underneath the car, grip the propshaft and try and turn it clockwise/anti clockwise. If there's any movement - it's worn.

The link below is of generic images

propshaft universal joint Google Search

Mrs Amanda when you said on pushing the gas pedal is shaking do you mean the whilst accelerating with engine running ( reving) you do receive a shake? or when pushing the pedal you do feel on the pedal with engine off a shake? If it is the first check for any spark plug or spark plug HT Lead not working and cause the engine to shake. If is the second cause then check for your pedal connection cable etc.

check the engine mounts.

a good thing to check would be your inner and outer tie rod ends. if they are going bad they will cause a lot of shaking in the car and will also cause the front end to be out of a lined which will make your tires wear faster and uneven

yes. if the axle is bad and binding it can cause the front end to vibrate because it gets out of balance.

COULD HAVE LOW AND HIGH SPOTS IN THE BRAKE ROTORS.CHECK TIRES FOR DEFECTS.COULD NEED FRONT END ALIGNMENT OR BAD WHEEL BEARINGS CAUSE WHEELS VIBRATION.

when you accelerate the torque(twisting motion)is lifting the front of the car(hence wheelspin), taking the weight off the lower control arms(no weight = more movement)so when you coast, the full front end weight is on the front suspension = no shake....

no, idle air control valve is literally to control your idle speed.
what happen when you press on gas? car shakes, RPM goes up, or engine just bogs down?

u need a front end alignment

Most likely with this problem is the front tires. The tires maybe " out of balance " or " out of round " causing the vibration at certain speeds.