Dan AndersonHow do you teach completing the square? A, B, or something different?
For what it’s worth half my precalc class uses A and half use B. I’ve always taught B, but I don’t really care which method they choose.
Markus Redeker 🐘@dandersod Method A should be how you teach it, I think, because it shows more clearly why the method works. (It is the general principle of “taking away and giving it back”, in this case of the number 64.)
Now thinking about it, I believe that you should write the second line of A as
\[ y = \frac12 (x^2 + 16x + 64 - 64 + 44), \]
to make the intent even clearer.
Method B too should be admissible, of course.
@dandersod Another thought about completing the square: It is helpful to know explicitly the following variant of the binomial formula,
\[ x^2 + a x + \tfrac14 a^2 = (x + \tfrac12 a)^2, \]
because it shows more clearly which number is needed when completing the square.