Bad shocks as well as bad struts can cause loose steering and have a detrimental effect on steering as well as the stopping and stability of the vehicle.
Common signs of bad shocks are leaking fluid on exterior of shocks and struts, unusual noises, vibration in the steering wheel, rear squat during acceleration, uneven tire wear, vehicle rolling or swaying when cornering, bouncy ride and nose dive when braking.
Bad shocks can indeed be a cause of vibration when you're braking.
However most times if the shocks are the problem with the cause of vibration then the vibration may continue while driving.
Another cause of vibration of a vehicle while braking is a sticking brake caliper or even warped brake rotors.
The most common cause of a car shaking when going over 45 MPH is an out of balance tire.
You tire could be wearing out unevenly causing the out of balance on the tire or you may have even lost a wheel balancing wheel weight.
Look at your tire and see if it looks out of round and if so then something such as your wheel bearings, shocks or struts etc could be causing the uneven tire wear.
Also jack the vehicle up and spin the tire by hand and watch it and look to see if it's out of round and if so you'll notice the top of the tire will look like it's going higher and then lower as it rotates.
A bad brake caliper that is sticking could also cause the car to shake at 45 MPH or above and also warped brake rotors as well.
Get the car checked out because the car should not shake at all especially when going over 45 MPH.