I'd like to perform polynomial regression on my data (which lies in [0,10]), but I need to ensure that the endpoints of the range are fixed, i.e. that the curve goes through (0,0) and (10,10). So the interpolant
$y = a + bx + cx^2 + \epsilon$
$y = bx + cx^2 + \epsilon$ with $b = 1 - 10c$.
Assuming just quadratic for now, although I might go to a cubic if the data warrants it. But how do I express this constraint during fitting?