Problem with fitting simple quadratic function to 3 data points

[johnismint]

Hello PF,

Ok so here is my problem. I have an array of data points which are the chi^2 values for a fit I have performed. I wish to calculate the 1-sigma error for this fit, so I figure I could find the lowest chi^2 value, and the two points either side that value, and fit a quadratic function to this. Then 'fill' this such that deltachi^2=1 and calculate the deviations either side. But this is somewhat irrelevant for now...

I have a complete mental block, and I'm really struggling to figure out how to fit a quadratic to these 3 data points. I'm editing a fortran-77 program to do this (which I'm not that familiar with) so would like to keep it as simple as possible. If my function is F(x)= a*x**2 + b*x + c, I already have c constrained to be my minimum value, however, I can't seem to figure out how to get these other co-efficients. I know there are methods such as Cramer's rule, however this would require significant changes to the program, which I would like to avoid. Can anyone think of an easier way to implement this?

Many thanks

 

[rochfor1]

If you plug in each of your data points, you'll get three linear equations in three unknowns (a, b, c). Then it's just a bit of linear algebra.

 

[GoldPheonix]

There's the Lagrange Polynomial:

http://en.wikipedia.org/wiki/Lagrange_polynomial

But I don't know right now if there are more effective polynomial interpolations. Read up on more general formulas/algorithms:

http://en.wikipedia.org/wiki/Polynomial_interpolation

 

[Gib Z]

If you plug in each of your data points, you'll get three linear equations in three unknowns (a, b, c). Then it's just a bit of linear algebra.

I think that's what he was referring to by Cramer's Rule in his original post, he doesn't want to do that.