Let $V = P_2$. Consider the linear functional $\phi(p) = p(1) + p'(0)$. Find the polynomial $q \in P_2$ such that $\phi(p) = \langle p, q \rangle$ using the inner product $\langle p, q \rangle = a_0 b_0 + a_1 b_1 + a_2 b_2$.