### Cubic Spin

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

### Sine Problem

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.

### Parabolic Patterns

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

# Cubics

##### Stage: 4 and 5 Challenge Level:

This pattern of graphs is the creation of Ali Abu-Hijleh, from Riccarton High School, Christchurch, New Zealand. Two of the equations are: $$y=(x+6)^3-2$$ $$y=-(x-9)^3+3$$

Find the equations of the other 12 graphs in this pattern.

You could use a graphic calculator or graphing software. For example, you can download Graphmatica for free from here and it comes with a good help file.

Draw your own pattern of graphs.