Answer
Center: $(-2,-2)$ $;$ Radius: $2$
Domain: $[-4,0]$ $;$ Range: $[-4,0]$
The graph is:
Work Step by Step
$(x+2)^{2}+(y+2)^{2}=4$
The standard form of the equation of a circle is $(x-h)^{2}+(y-k)^{2}=r^{2}$, where $(h,k)$ is the center of the circle and $r$ is its radius.
From the equation given, it can be seen that $(h,k)=(-2,-2)$ and that $r^{2}=4$
The center of the circle is $(-2,-2)$
The radius of the circle is:
$r^{2}=4$
$\sqrt{r^{2}}=\sqrt{4}$
$r=2$
From the equation's graph (shown below), it can be seen that its domain is $[-4,0]$ and its range is $[-4,0]$
