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**pickslides** **Q1. Find the equation of the form $\displaystyle y=a(x-h)^3+k$ 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 $\displaystyle y=a(x-24)^3+9$. Now substituting in (60,10) to find the dialation factor 'a'.

$\displaystyle 10=a(60-24)^3+9$

$\displaystyle 10=a(36)^3+9$

$\displaystyle 10=46656a+9$

$\displaystyle 1=46656a$

$\displaystyle a=\frac{1}{46656}$

therefore giving $\displaystyle y=\frac{1}{46656}(x-24)^3+9$

**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?