Answer
The x-intercept is (0,0)
The y-intercept is (0,0)
The equation has symmetry only with respect to the x-axis.
Work Step by Step
To find the x-intercept, we set y to 0 and solve for x:
$2x=3(0)^2$
$2x=0$
$x=0$
To find the y-intercept, we set x to y and solve for y:
$2(0)=3y^2$
$0=y^2$
$y=0$
To test for symmetry with respect to the x-axis, we substitute y for -y and check if it equals the original equation:
$2x=3(-y)^2$
$2x=3y^2 \checkmark$
To test for symmetry with respect to the y-axis, we substitute x for -x and check if it equals the original equation:
$2(-x)=3y^2$
$-2x=3y^2$ nope
To test for symmetry with respect to the origin, we substitute x for -x, substitute y for -y and check if it equals the original equation:
$2(-x)=3(-y)^2$
$-2x=3y^2$ nope