Coordinate Geometry and Graphs

Parabolic Patterns

Age 14 to 18 Challenge Level:

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

Age 16 to 18 Challenge Level:

This is a beautiful result involving a parabola and parallels.

Intersections

Age 14 to 18 Challenge Level:

Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?

Tangled Trig Graphs

Age 16 to 18 Challenge Level:

Can you work out the equations of the trig graphs I used to make my pattern?

Curve Match

Age 16 to 18 Challenge Level:

Which curve is which, and how would you plan a route to pass between them?

Erratic Quadratic

Age 16 to 18 Challenge Level:

Can you find a quadratic equation which passes close to these points?

Whose Line Graph Is it Anyway?

Age 16 to 18 Challenge Level:

Which line graph, equations and physical processes go together?