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Guide and features
Science, Technology, Engineering and Mathematics
Featured Early Years Foundation Stage; US Kindergarten
Featured UK Key Stage 1&2; US Grades 1-4
Featured UK Key Stage 3-5; US Grades 5-12
Featured UK Key Stage 1, US Grade 1 & 2
Featured UK Key Stage 2; US Grade 3 & 4
Featured UK Key Stages 3 & 4; US Grade 5-10
Featured UK Key Stage 4 & 5; US Grade 11 & 12
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Curve Fitter 2
Can you construct a cubic equation with a certain distance between its turning points?
I wish to find a function which passes through the origin and only has turning points at $(1, 2)$ and $(2,1)$, as in the following sketch:
What sorts of equations would be good candidates for having a graph of this form? Can you definitely rule out certain types of equation from having a graph like this?
Although this curve might look like a cubic equation, it actually cannot be a cubic equation. Prove that this is the case.
Next, can you explicity find an equation which exactly satisfies these conditions and looks similar to the graph shown (i.e. with no other turning points anywhere and the same asymptotic behaviour)? How might you assess the effectiveness of the 'similarity'?
Families of Graphs
Transformation of functions
Meet the team
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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