Graph sketching

Use the interactivity to move Pat. Can you reproduce the graphs and tell their story?

This problem challenges you to sketch curves with different properties.

This problem challenges you to find cubic equations which satisfy different conditions.

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

Can you massage the parameters of these curves to make them match as closely as possible?

Can you work out which processes are represented by the graphs?

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?