Gradual curve change with graph mapper?

Hello,

I have been experimenting with Grasshopper for some time but run now into a problem I cannot seem to solve. I am using the graph-mapper to create a parabolic curve (through points) which I placed along a second curve.

Now I want the parabolic curve to chance shape gradually along the second curve: I want to the first of many parabolic curves to have a different curvature than the last. (in the graph-mapper this would mean my first curve has different slider settings than my last curve)

I don't think this is going to be possible with the graph-mapper because there is no input for changing the curvature (just the sliders) But is this possbile with a parabolic expression or an extension? Or even by a slow manual rhino operation? 

Any help is very much appreciated! I hope it is clear what im trying to do (language barrier is making it difficult for me)

Curve.gh