Question

for the given equation list the intercepts and test for symmetry
y = x^3 -512

Answer 1

You know what the graph of x^3 looks like, so this one is just the same curve shifted down by 512 units.

One x-intercept at x=8
one y-intercept at y=-512
no symmetry, since the function is neither even nor odd.

Actually, there is radial symmetry about the point (0,-512) but that is not usually the intent.