Curve Fitter 2

Age 16 to 18 Challenge Level:

Why do this problem?

This problem draws learners into ideas concerning curve fitting and the way in which curve fitting problems can be greatly simplified by using 'sensible' coordinate systems and the way in which length-preserving transformations can be used to create these.

Possible approach

An important part of this problem is students coming to the realization that the problem is greatly simplified by choosing the right sorts of coordinates. Students might benefit from doing this question individually and it might make a good starter activity to return to once students have had a chance too think about it.

Key questions

How can the transformations be used to create a 'simple' cubic equation?

Possible extension

The extension referred to in the equation is very interesting. You might like to inform students that there is in fact an algebraic solution to any cubic equation, which they might use in this problem.

Possible support

One way into this problem might be to draw a few simple cubic equations, find their turning points and then work out the squared distance between them. Alternatively, first try the easier problem Curve Fitter which will start to get students to think about cubic equations and turning points.