For the Quadratic Function $P(x)=-3 x^{2}-6 x+9$ Do Each of the Following

Essay

For the quadratic function $P(x)=-3 x^{2}-6 x+9$ do each of the following.
(a) Find the vertex using an analytic method.
(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 interval over which the function is increasing, and the interval over which it is decreasing.