$$y^{2}=\frac{q}{4}$$
$q=4y^{2}$
$y=-\frac{\sqrt{q}}{2}$
$y=\frac{\sqrt{q}}{2}$
$y=\frac{\sqrt{q}}{2}$
$y=-\frac{\sqrt{q}}{2}\text{, }q\geq 0$