The related work page compares the method described by Savage, with the method that I proposed. In particular, my approach's avoidance of an extra assumption in Completing the Square was not achieved by Savage's method. His approach overlapped in almost all calculations, with a pedagogical difference in choice of sign, but had a difference in logic, as (possibly due to a friendly writing style which leaves some logic up for interpretation) it appears to use the additional (true but significantly more advanced) fact that every quadratic can be factored into two linear factors, or has some reversed directions of implication that are not technically correct. The combination of these steps is something that anyone could have come up with, but after releasing this webpage to the wild, the only previous reference that surfaced, of a similar coherent method for solving quadratic equations, was a nice article by mathematics teacher John Savage, published in The Mathematics Teacher in 1989. The individual steps of this method had been separately discovered by ancient mathematicians. Known thousands of years ago (Babylonians, Greeks) Thus − B 2 ± uwork as rand s, and are all the roots.Two numbers sum to − Bwhen they are − B 2 ± u.If you find rand swith sum − Band product C, then x 2 + B x + C = ( x − r ) ( x − s ), and they are all the roots.Alternative Method of Solving Quadratic Equations One night in September 2019, while brainstorming different ways to think about the quadratic formula, I was surprised to come up with a simple method of eliminating guess-and-check from factoring that I had never seen before. (Public Domain N.Mori).I've recently been systematically thinking about how to explain school math concepts in more thoughtful and interesting ways, while creating my Daily Challenge lessons. Thumbnail: Plot of the quadratic function. 9.8: Graph Quadratic Functions Using Transformations.9.7E: Graph Quadratic Functions Using Properties (Exercises).9.7: Graph Quadratic Functions Using Properties.
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