A parent function is a bit of a vague term I think BUT it is a simpler graph that gives the basic shape of the function in question.
For instance, the parent function of y=cos(2x)+3 could be considered to be y=cos(x)
I think it could also be considered to be y=cos(2x) but I think some people might disagree with this one. ://
Here is the graph that I have 'built up from tyhe parent function