Answer
$y^2=\frac{4}{3}x$
Work Step by Step
Since, the parabola is symmetric with respect to the $x-$axis, it means that the parabola is opening to the right or left side.
The standard form of a horizontal parabola is given as: $y^2=4px ~~~(1)$
(when the parabola has the vertex at origin $(0,0)$)
Here, the point $(3,2)$ is on the graph, so we have: $x=3; y= 2$
Now, we will plug the values of x and y in the standard form of parabola to determine the value of $p$:
$(2)^2=4p \times (3)$
or, $12p=4 \implies p=\frac{1}{3}$
Thus, the equation (1) becomes:
$y^2 =(4)\left(\frac{1}{3}\right) x \implies y^2=\frac{4}{3}x$
