f(x)=x³-1000=(x-10)(x²+10x+100).
Intercept is x=10.
Symmetry: y-intercept is -1000, and y=-1000 can be seen as a secondary x-axis. In relation to this secondary axis the curve is effectively f(x)=x³, where the secondary origin is (0,-10), and f(x)=-f(-x). There is no actual symmetry because the left and right sides of the curve are not mutual reflections.