Let $$f(x)= 1, \ g(x)=3 x + 9 \ \mbox{ and } \ h(x)=-6 x^2.$$ Consider the inner product $$\langle p,q \rangle= \int_0^{1} p(x)q(x) \, dx$$ in the vector space $C^0\lbrack 0,1\rbrack$ of continuous functions on the domain $\lbrack 0, 1 \rbrack$. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of $C^0\lbrack 0,1\rbrack$ spanned by the functions $f(x)$, $g(x)$, and $h(x)$.

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