Intersection of Piecewise curve fitting

How can I piecewise fit a curve, with two pieces, and find out the point of intersection of these two pieces? For example:

y = X+2, y<P y = x^2, y>=P

'P' is unknown and I want to find it.

And do I need additional Toolboxes besided the Curve Fitting Toolbox?

[Ana]

'y' is the function with which I want to fit my curve

[Lukas Bystricky]

If you're just interested in the intersection for this particular problem you can just set x+2 = x^2 and solve for x. (x = 2, -1). In general if you have equations for your curves you can use a nonlinear solver like fsolve.

[Torsten]

You really mean to distinguish between y<P and y>=P ?

Or is it x<P and x>=P ?

Best wishes

Torsten.

[Ana]

Hi Lukas and Torsten, thanks a lot for your comments. What I meant is, that I want to fit a curve by two different pieces: f(x)=a.x+b for the interval x<P and f(x)=c.x^(3/2)+d.x+e for x>=P. This P should the the intersection point of the two pieces that I want to fit into my original data curve. Thus, according to this intersection point, the coefficients of the pieces of the function to fit should be obtained.