Answer
The x-intercept is (1.875,0)
There are no y-intercepts
The equation has symmetry only with respect to the x-axis.
Work Step by Step
To find the x-intercept(s), we set y to 0 and solve for x:
$16(0)^2=120x-225$
$0=120x-225$
$120x=225$
$x=1.875$
To find the y-intercept(s), we set x to 0 and solve for y:
$16y^2=120(0)-225$
$16y^2=-225$
$\sqrt{16y^2}=\sqrt{-225}$
Taking the square root of a negative number is not possible. That means this equation has no y-intercepts.
To test for symmetry with respect to the x-axis, we substitute y for -y and check if it equals the original equation:
$16(-y)^2=120x-225$
$16y^2=120x-225 \checkmark$
To test for symmetry with respect to the y-axis, we substitute x for -x and check if it equals the original equation:
$16y^2=120(-x)-225$
$16y^2=-120x-225$ 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:
$16(-y)^2=120(-x)-225$
$16y^2=-120x-225$ nope