Q1. Find the equation of the form using the coordinates (0,0),(24,9) and (60,10) where (24,9) is the point of inflection.

It seems obvious that using (24,9) as the point of inflection gives . Now substituting in (60,10) to find the dialation factor 'a'.

therefore giving

Q2. Generalise your result to find a family of cubic equations that satisfy these conditions

As we have 3 fixed points in a cubic I cannot start to think how a family of curves can be formed given these conditions. Anyone have an idea?