From what I remember of linear algebra, a quadratic solution can be found as follows (sorry, this is going to be poorly formatted; I don't know how to combine super/subscripts and pre tags):

Given (x₁,y₁), (x₂,y₂)...(x_n, y_n) are your data points, a least squares solution can be found by creating a matrix A as such:
x₁² x₁ 1
x₂² x₂ 1
...
x_nⁿ x_n 1

and a vector b as such:
y₁
y₂
...
y_n
We then want to solve for a vector x = (A, B, C) such that:
A^TAx = A^Tb.
(Where A^T is the matrix transpose of A). The A, B, and C that you find by solving that equation will be the coefficients in the quadratic polynomial y = Ax² + Bx + C. If you know how to do matrix arithmetic, you should be able to swing it. I think that there are also modules on the CPAN that could help you with that.

thor