Hi i have a problem with quadratic splnes, i am supposed to find $S_1$ and $S_2$ that interpolates the following points S(-1)=0 S(0)=1 S(1)=2, and at the same time we want to find S such that $\int_{-1}^1 \! (S(x))^2 \, \mathrm{d}x.$ is minimal. The answer is on the form
$
S_1(x)=a_1 x^2 +b_1x +c_1$
on [-1,0] and
$
S_2(x)=a_2x^2 +b_2x +c_2$
on [-1,0]

I use the data points and find that a1=-a2, b1=b2 and c1=c2=1, but I have no idea how to use minimize $
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