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Quadratics Done Simply and Properly


A common middle school algebra topic like quadratics is all too often spread across hundreds of confusing textbook pages and several years of tedious instruction. It’s as if the subject is a mix of rocket science and neurosurgery. In reality, if you set aside some of the more beautiful geometric examples, the basic algebra of quadratic equations should not pose much of a problem for a typical math student. James Tanton confirms this with his Guide to Everything Quadratic [PDF], a short 64 page booklet on the fundamentals of quadratic equations. The guide presents the algebra of quadratics in an intuitive and mathematically sound way with plenty of examples. In addition to the algebra section, there is a section on graphing quadratics, and a section on fitting quadratics to data. As an added bonus, Tanton demonstrates a quick way to graph parabolas and includes a set of exercises that walk the reader through the derivation of the cubic formula, something that almost never appears in the standard school curriculum. If you want a more geometric perspective we recommend the book Lines and Curves. For those approaching quadratics for the first time, Tanton’s guide can replace or at least supplement most of the coverage of quadratics in a standard algebra textbook.