 ## An example of clutter

Here is a summary of what a standard textbook has to say about quadratic equations. I chose that particular book (Foster/Gell/Winters/Rath/Gordon, Algebra 1, Glencoe, McGraw-Hill, 1992, ISBN 0-675-13117) because I happen to have it in my office.
• Completing the square. (The only thing really needed.)
• The quadratic formula (which is derived by completing the square. But once that's understood deriving the quadratic formula only constitutes a mildly interesting exercise.)
• Solutions are x-intercepts. (By the way, what if the independent variable isn't called x? What if it's called y? In the latter case, if you rely on memorization the result is utter confusion.)
• Approximate solutions can be found by graphing. (Of course!)
• Solution by factoring. (I'd determine the factors by solving the equation.)
• The constant term after normalization is the product of the roots.
• The negative linear term after normalization is the sum of the roots.
• How to write a quadratic equation given its roots.
• Very many exercises, all of which are essentially the same, in which a particular pair of roots is found. (To be fair, there are also a number of more interesting questions.)

[16-Aug-1996]