interaction design – Interactive Graphing

I have a set of mathematical formulas that are more easily understood if viewed as graphs on a cartesian plane (each time fixing all of the parameters/variables but one). I want to add to a website an “applet” where users can generate those graphs and play a bit, so they can ask, for example, “how does the dependent variable u changes as a function of the independent variable x, if we fix q=0.5, a=2, beta=1.7 ?”

Ideally I would like the users to be able to:

  1. decide which variable to present as a function of which other variable.
  2. specify the parameter values using slide bars.
  3. overlap multiple graphs like these on the same coordinate system.
  4. use it without any web knowledge, of course.

Basically, I am thinking of a simple garphing calculator, like what Desmos are offering, except that it would be on our website with our design, and would have a pre-specified set of formulas to choose from.

Is there a good solution for this? (I hope this question is not too general to appear here, I can try to rephrase it more specifically if it is.)