On 26 June 2003 a debate in The House of Commons provided a response to a teacher’s comment that quadratic equations are irrelevant. In this talk we consider a variety of important applications ranging from the Babylonians’ use as a method of collecting tax to Travis Pastrana’s world record attempt to ‘jump’ a car across a river. We shall see that quadratic equations occur in some unexpected places and we shall show how a simple model of the population of bees in a hive leads to the idea of chaos.