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Grid Points on Hyperbolas
Age 16 to 18
Challenge Level 
The hint you need to help you to decide whether the hyperbola $y^2 - x^2 = k$ contains any points with integer coordinates is in the question What's Possible?
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Janusz Asked
In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?
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.
More Parabolic Patterns
The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.