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