#### Answer

$f(x)=x^{2}+2x+1$

#### 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 an axis of symmetry of $x=-1$ and that it opens upwards. Also, when plugging in the values to the equation $\frac{-b}{2a}$, you would also get $-1$. Therefore, $f(x)=x^{2}+2x+1$ is the correct answer.