### 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.

# Minus One Two Three

##### Stage: 4 Challenge Level:

Look at the two brackets for the factors that make the product. You are evaluating it for $x$ values of -1, -2, and -3 . Think what you could change systematically about those factors and see how it affects the size of the product for each of the three $x$ values.