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Converse
Clearly if a, b and c are the lengths of the sides of an equilateral triangle then a^2 + b^2 + c^2 = ab + bc + ca. Is the converse true?
Consecutive Squares
The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?
Parabolic Patterns
The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.
Stage: 4 Challenge Level: 
The mapping below was created using the NRICH Number Plumber.
Click here to watch a video explaining how to use the Number Plumber.
Click on the mapping to explore the relationship between the function and its graph.
Now replace the 1 and 3 with other values. How does this affect the graph?
What happens if you add instead of subtract?
Describe and explain any generalisations you make.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.