The question asks to construct a piecewise quadratic polynomial defined on the interval $\mathbb{R}$ of the form $ B_0= \begin{cases} p(x)=x^2,\qquad\qquad\quad\; 0\leq x<1,\\ q(x)=ax^2+bx+c,\quad\, 1\leq x<2,\\ r(x)=(3-x)^2,\qquad\quad 2\leq x<3,\\ 0\qquad\qquad\qquad\qquad\quad\,\text{otherwise} \end{cases} $
I need to find the coefficients for $q(x)$. However, I'm having trouble with figuring out which method to use. We're dealing with uniform quadratic B-splines. Would I need to use the Gram-Schmidt method?
Thanks.