A quadratic polynomial has zeros x=−1 and x=3. Its graph opens downward and passes through the point (0,6).
(a) Determine the explicit form of the polynomial.
(b) Find the coordinates of its vertex.
(c) Sketch a rough graph, indicating the intercepts with the coordinate axes and the vertex.
(d) From your results, state how many real zeros the polynomial possesses and justify your answer.