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.

Question

Quizplus · Accepted Answer

The Answer is (a)

(-1,12)

(b)
$(a) (-1,12) (b) (c) -3 ; 1 (d) 9 (e) domain: (-\infty, \infty) ; range: (-\infty, 12] (f) increasing: (-\infty,-1] ; decreasing: [-1, \infty)$
(c)

-3 ; 1

$(a) (-1,12) (b) (c) -3 ; 1 (d) 9 (e) domain: (-\infty, \infty) ; range: (-\infty, 12] (f) increasing: (-\infty,-1] ; decreasing: [-1, \infty)$ (d) 9
(e) domain:

(-\infty, \infty)

; range:

(-\infty, 12]

(f) increasing:

(-\infty,-1]

; decreasing:

[-1, \infty)

For the Quadratic Function P(x)=−3x2−6x+9P(x)=-3 x^{2}-6 x+9P(x)=−3x2−6x+9 Do Each of the Following

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