The graphs of three quadratic polynomials y=p1(x), y=p2(x) and y=p3(x) exhibit the following features in the xy–plane:
(i) For each of the cases (A), (B) and (C), state the exact number of distinct real zeros of the corresponding polynomial.
(ii) Denote the discriminants of the three polynomials by DA,DB and DC respectively. Arrange DA,DB and DC in increasing order, giving reasons for your answer.
(iii) Explain, with justification, how the position of the vertex of a parabola with respect to the x–axis helps in deciding the number of its real zeros.