#### Answer

domain$:\quad \mathbb{R}=(-\infty,\infty)$
range$:\quad (-\infty,-4] $

#### Work Step by Step

$f(x)= ax^{2}+b\mathrm{x}+c \quad $or $\quad f(x)=a(x-h)^{2}+k$
A quadratic function is defined for all real numbers,
domain$:\quad \mathbb{R}=(-\infty,\infty)$
The graph of f(x) is a parabola.
If the parabola opens down, the vertex is its maximum point.
At $x=-3$ the maximum of $f(x)$ is $-4.$
The range of f is $(-\infty,-4] $