Answer
The equation matches with the graph labeled as III.
Work Step by Step
It has the equation of a parabola with horizontal axis: $y^2=4px$
$y^2=2x$
$4p=2$
$p=\frac{1}{2}$
$p\gt0$. Parabola opens to the right.
When $x=1$
$y^2=2(1)=2$
$y=±\sqrt 2$
So, the parabola passes through the points $(1,±\sqrt 2)$
The equation matches with the graph labeled as III.
