You may also like

problem icon

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?

problem icon

How Many Solutions?

Find all the solutions to the this equation.

problem icon

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

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.