All Cubic Polynomials Are Point Symmetric

It was accident that I stumbled upon this PDF file discussing point symmetry in cubic polynomials. I had been looking for information about sketching cubic polynomials that could help a student I am currently tutoring in Mathematics. I've extracted the key observation in the screen shot below:

Here is an annotated graph that I produced in GeoGebra illustrating the point of symmetry for a specific cubic polynomial: \(\ f(x)=x^3-3x^2+2x-1\)

A translation of the graph (-1, 1) to (0, 0) makes the graph symmetry about the origin and an odd function. The new equation is calculated as follows: \(\ f(x)-1=(x+1)^3-3(x+1)^2+2(x+1)-1\) and \(\ f(x)=x(x+1)(x-1)\) or \(\ f(x)=x(x^2-1)\).