List

Coordinate Geometry and Graphs

Parabolic Patterns
problem
Favourite

Parabolic Patterns

Age
14 to 18
Challenge level
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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.

Parabella
problem
Favourite

Parabella

Age
16 to 18
Challenge level
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This is a beautiful result involving a parabola and parallels.

Intersections
problem
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Intersections

Age
14 to 18
Challenge level
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Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?
Tangled Trig Graphs
problem
Favourite

Tangled Trig Graphs

Age
16 to 18
Challenge level
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Can you work out the equations of the trig graphs I used to make my pattern?

Curve match
problem

Curve match

Age
16 to 18
Challenge level
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Which curve is which, and how would you plan a route to pass between them?
Erratic quadratic
problem

Erratic quadratic

Age
16 to 18
Challenge level
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Can you find a quadratic equation which passes close to these points?