| | | Exercise on formatting equations |
Write an explanation, suitable for high school students, about
the method of completing the square. Include each of the following items:
(i) inline mathematics, (ii) a displayed, numbered equation,
(iii) a reference to a numbered equation, and (iv) a multi-line
displayed formula with equations aligned on equals signs. (If
you are using LaTeX, you should generate the reference number
in item (iii) automatically by using LaTeX's \ref
command.) Also pay attention to using logical
formatting rather than
visual formatting.
The point of this exercise is not only to practice formatting mathematics, but also to practice principles of good exposition. Keep in mind that you are trying to communicate with a hypothetical teenager, not with your instructor.
By the way, what reasons can you
think of for teaching the topic of completing the square, when
Maple can do it automatically? (See
the illustration.)
To avoid making embarrassing mistakes, you may want to use
Maple to check the examples that you put in your paper.
The LaTeX code for the formula in the illustration is
10 \left( x + \frac{7}{20} \right)^2 + \frac{71}{40}
(inside mathematics mode).
You will encounter a feature of LaTeX that may be new to you in this exercise: you are going to get a warning message about undefined references. The first time through a file, LaTeX takes note of symbolic cross references and writes them into an auxiliary file named filename.aux; the second time through, LaTeX inserts the cross references. Thus, you will need to execute the command "latex filename" twice before printing your file.
The Math 696 course
pages were last modified April 5, 2005. | | | Exercise on formatting equations |