Answer
$j(x)=-x^{2}-1$
Work Step by Step
$f(x)=x^{2}+2x+1$
$g(x)=x^{2}-2x+1$
$h(x)=x^{2}-1$
$j(x)=-x^{2}-1$
First, you will notice that the graph has a y-intercept of $-1$ and that it opens downwards. Therefore, $j(x)=-x^{2}-1$ is the correct answer.