If f(0) = 0, f(1) = 1, f(2) = 5 , and ax^2+bx+c=0, what is the value of f(3)?
f(0) = a (0^2) + b(0) + c = 0 shows that c =0
f(1) = a(1^2) + b(1) =1 so a + b = 1
f(2) = a(2^2) + b(2) = 5 so 4a + 2b = 5
solving these two equations results in a = 3/2 b = - 1/2
f(x) = 3/2 x^2 -1/2 x
f(3) = 3/2 (3^2) - 1/2 (3) = 12