Answer
x-intercept: $(-2,0), (0,0), (2,0)$
y-intercept: $(0,0)$
symmetry: origin
Work Step by Step
x-intercept:
$0=x^3-4x$
$0=x(x^2-4)$
$0=x(x-2)(x+2)$ [difference of squares]
$x=-2,0,2$
y-intercept:
$y=0^3-4*0$
$y=0$
y-axis symmetry:
$y=(-x)^3-4(-x)$
$y=-x^3+4x$
asymmetrical
origin symmetry:
$-y=(-x)^3-4(-x)$
$-y=-x^3+4x$
$y=x^3-4x$
symmetrical
