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,
McGrawHill, 1992, ISBN 067513117) 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 xintercepts. (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
[16Aug1996]