Answer
a.
$x$ intercept: $(1.875,0)$
$y$ intercept: no $y$ intercept
b.
Symmetry about the $x$ axis: Symmetry about the $x$ axis
Symmetry about the $y$ axis: No symmetry about the $y$ axis
Symmetry about the origin: No symmetry about the origin
Work Step by Step
a.
For $x$ intercept:
$16(0)^2=120x - 225$
$0=120x - 225$
$225 =120x$
$1.875=x$
Therefore, $(1.875,0)$
For $y$ intercept:
$16y^2=120(0)-225$
$16y^2=-225$
$y = \sqrt \frac{-225}{16}$
$y = undefined$
Therefore, no $y$ intercept
b.
Test for symmetry with respect to the $x$ axis:
Replace $y$ with $-y$ in the equation
$16(-y)^2 = 120x - 225$
$16y^2 = 120x - 225$
Since replacing $y$ with $-y$ gives the same equation, the equation$16y^2 = 120x - 225$ is symmetric with respect to the $x$ axis.
Test for symmetry with respect to the $y$ axis:
Replace $x$ with $-x$ in the equation
$16y^2 = 120(-x) - 225$
$16y^2 = -120x - 225$
Since replacing $x$ with $-x$ DOES NOT gives the same equation, the equation $16y^2 = 120x - 225$ is NOT symmetric with respect to the $y$ axis.
Test for symmetry with respect to the $origin$:
Replace $x$ with $-x$ and $y$ with $-y$ in the equation
$16(-y)^2 = 120(-x) - 225$
$16y^2 = -120x - 225$
Since replacing $x$ with $-x$ and $y$ with $-y$ DOES NOT gives the same equation, the equation $16y^2 = 120x - 225$ is NOT symmetric with respect to the $origin$
Therefore, the equation is symmetry about the $x$ axis
