7. Any cubic function in one variable looks like f (x) = c323 + c2x2 + cix + co for some co, C1, C2, C3 E R. (a) Write the equation (in co, C1, C2, C3) which determines when the point (3, 2) is on the graph of f (x). (Recall that (a, b) is on the graph of f (x) whenever b = f(a)). (b) Is your answer to (a) a linear equation in the ci's? (c) Write the linear system of equations in co, . .., 3 whose solution are all (co, C1, C2, C3) such that the graph of f (x) = c32 + c2x2 + cix + co goes through the points P = {(4, -1), (1, 0), (2, 1), (3, 2) }. (d) Solve the linear system from part (c) and write down the cubic f(x) whose graph goes through each of the points in P