Arcing and object along the X axis with a random amount

Is there a simple way to arc an object along the X axis and have it arc out a random amount? In other terms, can I arc an object's X axis from point A to point B with a random middle point to curve out to? The problem with the random point is that I need this to run in Update() and it needs to run on multiple objects so I can't use Random in Update() because it keeps randomizing the point every frame and I can't use a global Random value because the other objects also need unique random values.