Answer
$a.\quad $see image
$ b.\quad$
The domain is $(-\infty,\infty)$
The range is $[-\infty, 9)$
$ c.\quad$
Increasing on $(-\infty,3)$
Decreasing on $(3,\infty)$
Work Step by Step
$f(x)=-x^{2}-6x$
$a=-1,b=-6,c=0$
$ a.\quad$
Leading coefficient is negative - opens down.
Vertex:
$x=\displaystyle \frac{-b}{2a}=\frac{-(-6)}{2(1)}=\frac{6}{2}=3$
$f(3)=-9+18=9$
Vertex: $(3,9)$
Axis of symmetry: the line $x=3$
Zeros $(x-$intercepts):
$-x^{2}-6x=0$
$-x(x+6)=0$
$x=0$ or $x=-6$
$x-$intercepts: $(0,0),(-6,0)$
y-intercept: (0,c)$ = (0,0)$
$ b.\quad$
The domain is $(-\infty,\infty)$
The range is $[-\infty, 9)$
$ c.\quad$
Increasing on $(-\infty,3)$
Decreasing on $(3,\infty)$
