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Real(ly) Numbers

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

How Many Solutions?

Find all the solutions to the this equation.

On the Road

Four vehicles travelled on a road. What can you deduce from the times that they met?

Parabolas Again

Age 14 to 18 Challenge Level:

Here is a pattern for you to experiment with. This one is composed of the graphs of 14 parabolas. You may like to use a graphic calculator or graph drawing software to do this question. For example you can download Graphmatica for free from http://www.graphmatica.com/

The equations of three of the graphs are: $$y=2(x-6)^2-4$$ $$y=2x^2 -1$$ $$y= -2(x-4)^2 +3$$

Graph of equations.

Find the equations of the other 11 graphs in this pattern. Draw your own pattern and send it to us.