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More Parabolic Patterns

The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.

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Ellipses

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On the Road

Age 14 to 16 Challenge Level:

Four vehicles travelled on a road with constant velocities.

The car and the scooter were travelling in one direction whilst the bike and the motorcycle travelled in the opposite direction.

The car overtook the scooter at 12:00, then met the bike at 14.00 and the motorcycle at 16.00.
The motorcycle met the scooter at 17.00 then it overtook the bike at 18.00.

At what time did the bike and the scooter meet?