Ignition coil
 

2005 Ford F-150 5.4 3v, rough idle, I checked under the hood noticed the coolent was low, topped it off to the fill line, I noticed the ignition coil was shaking around after burping the radiator. Checked it and noticed the hole the ignition coil bolts to was broke off. What do the ignition coils bolt to? So I know what to replace.

Some coil set-ups used that bolt to make the ground for the coil.

I don't believe you want to get involved with replacing where the coils bolt to
Make sure the spark plug is in and torqued to spec. If the boot is worn from being loose , you could get a new boot to put on the coil and help keep it in place.
Have the plugs been replaced lately?