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.)
Fine print, your comments, more links, Peter Alfeld,
PA1UM
[16-Aug-1996]