Quadratic graphs are very familiar, but what patterns can you explore with cubics?
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Can you work out which processes are represented by the graphs?
This problem challenges you to find cubic equations which satisfy different conditions.
Sketch the members of the family of graphs given by $y = a^3/(x^2+a^2)$ for $a=1, 2$ and $3$.
Can you match the charts of these functions to the charts of their integrals?
Can you work out the equations of the trig graphs I used to make my pattern?
Which curve is which, and how would you plan a route to pass between them?
Which line graph, equations and physical processes go together?
