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