### 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.

Can you adjust the curve so the bead drops with near constant vertical velocity?

##### Stage: 4 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.
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