Hello All, I was hoping one of the many knowledgable people on this forum could give me some helpfull advice on how to proceed with the following problem. Basically, I am trying to fit experimental data to a curve. In general my curve looks like this and I know the constants have the following constraints. I also know the range and domain of the function over the area I am interested in. f(x)=a*(x^2)+b*x+c, 0<=f(x)<5, 0<x<50, -1<a<0, 0<b<1 I have never seen a negative c and I think the following should hold, |a|<|b|, but I would rather not rely on either if possible. Oh ya, this is probably obvious but just in case, x is the variable I can control well and f(x) is the measured value. Also, I can vary x over the entire domain given and take many measurements. a, b, and c are constant for one particular setup but will change when I physically change the setup (i.e. switch to new components). Anyway, this system is linear and quite easy to deal with. Unfortunately this is a sort of a reduced setup. I'll call it Experiment 1. What I really want is Experiment 2 which changes my characteristic equation to: f(x)=a*(x+p)^2+b*(x+p)+c Unfortunately I cannot control p or measure it directly (actually if I change to an experiment 3 I can, but there are good engineering reasons to try to avoid doing so. It is also a lot of work and this experiment needs to be repeated many times for different setups so time spent here could result in significant time savings overall) Anyway, I do know its possible range, 0<p<2. The other constraints still apply. Oh ya, p will be constant throughout the setup as well. I believe this system is non-linear (because two unknowns are multiplied together) and I know there are iterative methods to solve such a system but I know very little about them. I am sure this is a solved problem. Does someone know the name of the solution or technique to solve it? I did do a little googling before writing this post and found some info on root finding. Is this a good technique to try? Perhaps there is some nifty variable substitution I am not seeing that could reduce this to a linear case?