Answer
$y^2=-3x$
Work Step by Step
Equation of a parabola with horizontal axis: $y^2=4px$
The parabola passes through the points $(p,±\frac{3}{2})$. Let' use the point $(p,\frac{3}{2})$:
$(\frac{3}{2})^2=4p(p)$
$\frac{9}{4}=4p^2$
$p^2=\frac{9}{16}$
$p=±\frac{3}{4}$
The parabola opens to the left. Focus is on the negative x-axis. So, $p$ is also negative:
$p=-\frac{3}{4}$
$y^2=4px$
$y^2=4(-\frac{3}{4})x$
$y^2=-3x$
