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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.

Parabolas Again

Age 14 to 18
Challenge Level


Here is a pattern for you to experiment with. This one is composed of the graphs of 14 parabolas. You may like to use a graphic calculator or graph drawing software to do this question.


The equations of three of the graphs are: $$y=2(x-6)^2-4$$ $$y=2x^2 -1$$ $$y= -2(x-4)^2 +3$$

Graph of equations.

Find the equations of the other 11 graphs in this pattern. Draw your own pattern and send it to us.