The object of the present article is to indicate the scope of graphical methods and the desirability of using them far more extensively in teaching elementary mathematics. Articles indicating some of the possibilities have appeared recently in the Mathematical Gazette, one by Dr. W G. Bickley, “Arithmetic, Algebra, and Calculus on the Drawing Board”, May 1941, Vol. XXV, No. 264, and another by C. Dudley Langford, “A graphical method of solving problems on ‘Rate of Work’ and similar problems”, Dec. 1941, Vol. XXV, No. 267. Graphical work is so universal in its application that it is impossible to deal with more than a very small section of work in the compass of a single article, and “Quadratic Equations” has been chosen for purposes of illustration. Through the medium of graphical methods and concrete numerical illustrations, the elementary student of mathematics gets a much clearer and more interesting view of the subject.