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### 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.

### Exploring Cubic Functions

Quadratic graphs are very familiar, but what patterns can you explore with cubics?

##### Age 14 to 16 Short Challenge Level:

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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.