Sequences And Series

Let for \(f(x) = {a_0}{x^2} + {a_1}x + {a_2},\,f'(0) = 1\) and \(f'(1) = 0\). If a₀, a₁, a₂ are in an arithmatico-geometric progression, whose corresponding A.P. has common difference 1 and corresponding G.P. has common ratio 2, then f(4) is equal to _____________.