Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational symmetry. Do graphs of all cubics have rotational symmetry?

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

Knowing two of the equations find the equations of the 12 graphs of cubic functions making this pattern.

Find the relationship between the locations of points of inflection, maxima and minima of functions.

Can you construct a cubic equation with a certain distance between its turning points?

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?