$y=-\frac{\sqrt{x}\sqrt{x+2}}{2}$
$y=\frac{\sqrt{x}\sqrt{x+2}}{2}$

$x=\sqrt{4y^{2}+1}-1$
$x=-\sqrt{4y^{2}+1}-1$

$y=\frac{\sqrt{x\left(x+2\right)}}{2}$
$y=-\frac{\sqrt{x\left(x+2\right)}}{2}\text{, }x\leq -2\text{ or }x\geq 0$