Ummm... I think you have forgotten more than that to which you are admitting.
x and y are variables related to a Cartesian Coordinate System
a, b, and c are parameters that require additional information in order to pin down. They can be virtually anything. They do not have specifc names or purposes unless you specify a particular application or purpose.
"slope", as a single, fixed entity, has no meaning for a parabola. It changes all the time.
So, for real, what exactly was your question? Perhaps a problem statement would be beneficial?