Answer
$f(x)=(x+1)^2-1$
Work Step by Step
Completing the square:
$f(x)=x^2+2x$
$f(x)=x^2+2x+(\frac{2}{2})^2-(\frac{2}{2})^2$
$f(x)=x^2+2x+1^2-1^2$
$f(x)=(x+1)^2-1$
Graphing the function:
1st step (black graph): The parent function: $y=x^2$
2nd step (green graph): Shift down by 1 unit. $y=x^2-1$
Final step (blue graph): Shift left by 1 unit. $y=(x+1)^2-1$