Let $$f(x)= -6, \ g(x)=-6 x + 5 \ \mbox{ and } h(x)=9 x^2 + 3 x - 2.$$ Consider the inner product $$\langle p,q\rangle =p(-1)q(-1) + p(0)q(0) + p(1)q(1)$$ in the vector space $P_2$ of polynomials of degree at most $2$. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of $P_2$ spanned by the polynomials $f(x)$, $g(x)$ and $h(x)$.

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