Answer
The $x$-intercept is $0$.
The $y$-intercept is $0$
The graph of the equation is symmetric about the $x$-axis.
Work Step by Step
To find the $x$-intercept, set $y=0$ then solve for $x$:
$2x=3y^2$
$2x=3(0)^2$
$2x=0$
$x=0$
Therefore, the $x$-intercept is $0$.
To find the $y$-intercept, set $x=0$ then solve for $y$:
$2x=3y^2$
$2(0)=3y^2$
$0=y^2$
$0=y$
Therefore, the $y$-intercept is $0$.
Test for symmetry with respect to the $x$-axis by substituting $-y$ to $y$ in the original equation:
$2x=3y^2$
$2x=3(-y)^2$
$2x=3y^2$
Since the result is the same as the original equation, then the graph of the the equation is symmetric about the $x$-axis
Test for symmetry with respect to the $y$-axis by substituting $-x$ to $x$ in the original equation:
$2x=3y^2$
$2(-x)=3y^2$
$-2x=3y^2$
Since the result is different from the original equation, then the graph of the equation is NOT symmetric about the $y$-axis
Test for symmetry with respect to the origin by substituting $-x$ to $x$ and $-y$ to $y$ in the original equation:
$2x=3y^2$
$2(-x)=3(-y)^2$
$-2x=3y^2$
Since the result is different from the given equation, then the graph of the equation is NOT symmetric about the origin.
