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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.

### Exploring Cubic Functions

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

# Closer to Home

##### Age 14 to 16 ShortChallenge Level

Consider the graphs with equations $y=2x-10$ and $y=x-6$.

Which comes closer to the origin?

Can you find the shortest distance between this line and the origin?

This problem is taken from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.