35The first reference to quadratic equationsappears to be made by the Babylonians in400 BC, even though they did not actuallyhave the notion of an equation. However,they succeeded in developing an algorithmicapproach to solving problems that could beturned into quadratic equations. Most of theproblems that the Babylonians worked oninvolved length, hence they had no conceptof a negative answer. The Hindumathematician, Brahmagupta, undertookmore work in the seventh century and herealised that negative quantities werepossible and he worked on the idea of lettersfor unknowns. In the ninth century, in hisbookHisab al-jabr w’al-muqabala,Al-khwarizmisolved quadratic equations entirely in words.The word "algebra" is derived from the titleof his book. It was not until the twelfthcentury that Abraham bar Hiyya ha-Nasifinally developed a full solution to aquadratic equation.USSR stamp featuring Al-khwarizmi2Quadratic Equations, Functions and Inequalities2.1Introduction to quadratic functionsConsider the curve What does it look like?To draw the graph a table of values can be set up on a calculator or drawn on paper.yx2.x01239410149y9410149x2123

2 Quadratic Equations, Functions and Inequalities36

2 Quadratic Equations, Functions and Inequalities37The maximum or minimumturning point is the pointwhere the curve turns and hasits greatest or least value. Thiswill be looked at in the contextof other curves in Chapter 8.