I have come up with :
a*P0(x) + b*P1(x) + c*P2(x) where a=1.175201 ; b=1.103638 ; c=0.357814
P0(x), P1(x), P2(x) are Legendre polynomials.
This result is the same as :
A + B*x + C*x² where A=0.996294 ; B= 1.103638 ; C=0.536722
Classical polynomial regression leads exactly to the same result.
In order to find where is the mistake in your calculus, you should show the details of what you did.