Answer
$y=\frac{1}{(x+2)^2}-1$
$\:$
$ $
Work Step by Step
$y=\frac{1}{x^2}$
Moving the graph down by $\ 1\ $ unit will change the $\ y\ \rightarrow\ y+1$. And moving it to the left by $\ 2 \ $ unit will change the $\ x\ \rightarrow\ x+2.$
So the equation of the shifted graph would be:
$y+1=\frac{1}{(x+2)^2}$
$y=\frac{1}{(x+2)^2}-1$