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
Find all the solutions to the this equation.
Four vehicles travelled on a road with constant velocities. The car
overtook the scooter at 12 o'clock, 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?
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 here .
The equations of three of the graphs are: $$y=2(x-6)^2-4$$
$$y=2x^2 -1$$ $$y= -2(x-4)^2 +3$$
Find the equations of the other 11 graphs in this pattern. Draw
your own pattern and send it to us.