Is there a C++ graphing library that can display visual graphs (such as hyperbolas and parabolas and linear equations) based on the equation it is given and that is cross platform? Or am I just asking for too much...
Let's take your question step by step.
"based on the equation [that] it is given" This would require you to write an expression parser; C++ cannot interpret equations "on the fly" without you writing a procedure to do so. For this, I recommend you look at Bison (go straight to the example RPN calc to get the idea).
For the libraries, you can get any GUI toolkit for C++; there are dozens; the recommendation for QT is probably the most honest one. Check also Wikipedia. You need any toolkit which will provide you with a canvas where you can paint or render lines or splines. This is not trivial, but also not difficult.
Your program would probably work as follows:
Again, this is not trivial but not difficult either.
You are reinventing the wheel, but I commend you for that.
Cheers,
J.