The graph of y=f(x), where f(x) is a polynomial of degree 3 , contains points A(2,4), B(3,9), and C(4,16). Lines A B, A C, and B C intersect the graph again at points D, E, and F, respectively, and the sum of the x-coordinates of D, E, and F is 24 . What is f(0) ?
Answer Choices
A. -2
B. 0
C. 2
D. \dfrac{24}{5}
E. 8