### 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 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?

# More Parabolic Patterns

##### Stage: 4 and 5 Challenge Level:

The illustration shows the graphs of twelve functions. Three of them have equations

$y = x^2$
$x = y^2$
$x = -y^2 + 2$

Use a graphic calculator or a graph drawing program to sketch these three graphs and then to locate them in this illustration. Use the clues given in this information to help you to find the equations of all the other graphs and to draw the pattern of 12 graphs for yourself. For your solution send in the equations you have found with an explanation of how you did it.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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