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