Answer
$y^2=x$
Work Step by Step
Equation of a parabola with horizontal axis: $y^2=4px$
The parabola passes through the point $(4,-2)$. Let' use the point $(4,-2)$:
$(-2)^2=4p(4)$
$4=16p$
$p=\frac{4}{16}$
$p=\frac{1}{4}$
$y^2=4px$
$y^2=4(\frac{1}{4})x$
$y^2=x$
