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In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

### 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

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

##### Stage: 4 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

The curve $y=x^{2}-6x+11$ is rotated through $180^\circ$ about the origin.

What is the equation of the new curve?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.