Answer
$a.\quad $see image
$ b.\quad$
The domain is $(-\infty,\infty)$
The range is $[-9,\infty)$
$ c.\quad$
Decreasing on $(-\infty,-1)$
Increasing on $(-1,\infty)$
Work Step by Step
$f(x)=x^{2}+2x-8$
$a=1,\ \ b=2,\ \ c=8$
$ a.\quad$
Leading coefficient is positive - opens up.
Vertex:
$x=\displaystyle \frac{-b}{2a}=\frac{-(2)}{2(1)}=-1$
$f(-1)=1-2-8=-9$
Vertex: $(-1,-9)$
Axis of symmetry: the line $x=-1$
Zeros $(x-$intercepts):
$x^{2}+2x-8=0\quad $... factors of -8 whose sum is 2...
$(x-2)(x+4)=0$
$x=-4$ or $x=2$
$x-$intercepts: $(-4,0),(2,0)$
y-intercept: (0,c)$ = (0,-8)$
$ b.\quad$
The domain is $(-\infty,\infty)$
The range is $[-9,\infty)$
$ c.\quad$
Decreasing on $(-\infty,-1)$
Increasing on $(-1,\infty)$