Prove that the graph of the polynomial
f(x) = x 3 - 6x 2 +9x +1
has rotational symmetry, find the centre of rotation and re-write the equation of the graph in terms of new co-ordinates (u,v) with the origin of the new co-ordinate system at the centre of rotation.
Do the same for the graph of the function g(x) = 2x 3 + 3x 2 +5x +4 .
Prove that the graphs of all cubic polynomials have rotational symmetry.