For the function do the following. (a) Find the vertex analytically. (b) Give...

For the function do the following.

(a) Find the vertex analytically.

(b) Give a comprehensive graph, and use a calculator to support your result in part (a).

(c) Find the zeros of P and support your result, using a graph for one zero and a table for the other.

(d) Find the y-intercept analytically.

(e) State the domain and range of P.

(f) Give the largest open interval over which the function is increasing and the largest open interval over which it is decreasing.