# Talk:Completing the Square

## Contents

#### Abram 7/7

This page is great. In the "Procedure for Completing the Square" section, maybe move everything starting with "Though the process of completing the square is finalized" into the hidden text aboove it. The problem with the current display is that this section refers to terms in an equation that you can't see unless you have expanded the hidden text or are currently looking at one of the mouseovers. Otherwise, this page is more than ready for public.

#### Anna 7/6

I gave you a $\neq$, some big parentheses where needed, and declared the page ready to go!

#### Abram 7/2

Great edits. The section on obtaining a perfect square trinomial is laid out very nicely.

In the section on "obtaining a perfect square trinomial", add a line showing that your final expression equals (x+5)^2 - 11, because that's really the end point we're after. You could even add a line at the end of this section summarizing once again the clever trick you have employed (I could also see a good argument for not adding this line).

I also wonder about the part of the "relationship between the terms" section that reads:

In general given the perfect trinomial and the equivalent squared binomial $x^2+bx+c=(x+d)^2$
Then $x^2+bx+c=x^2+2dx+d^2$
So,
$b=2d$
and
$c=d^2$
We can rearrange equalities to obtain the following: $c=(\frac{b}{2})^2$

Your algebra here is great, but you express the same ideas just as clearly in the preceding words. As a mathematician, I prefer the algebraic expressions to the verbal descriptions, but most people reading this page will probably prefer the words in the preceding bullet points. So for the sake of the average reader of this page, I would suggest deleting this bit of algebra, especially because the preceding bullet points really do say the same thing.

#### Abram 6/24

Tanya, I continue to be impressed by your organization of the page and the way it is clear at every moment what the "point" is of what you are writing. Your revisions have also made a big difference.

1) Small but important things (attend to these first -- you get lots of bang for your buck):

• Rewrite "This concept is important because in the process of completing the square, one of the components of the equation has to be a factored perfect square trinomial." What do you mean component? Also, make it clear that you "bring out" this "component" by manipulating this equation. It's not obvious to begin with.
• Add a little subsection on how to rewrite an arbitrary quadratic as the sum of a PST and a constant. This is the hardest part of completing the square, but you actually devote very little detail to it.

2) Most important big change is that readers who have struggled with completing the square will have trouble following some of your excellent, but implicit, reasoning. For example:

• In The Basics section explicitly state that any quadratic can be rewritten using a strategy you are about to explain. Otherwise, people are likely to be slow to recognize that you are describing a general method at the beginning, rather than exploring a specific quadratic.
• In general, $x^2-2ax+a^2=(x-a)(x-a)=(x-a)^2$ The quadratic on the left is a perfect square trinomial. It is the square of a binomial. This could be a bit more clear, because although you state the equation shows that x^2 - 2ax + a^2 is a PST, you could change your phrasing to make it clear that the whole point of this equation is that it proves this fact.
• The few lines leading up to We can rearrange equalities to obtain the following: $c=(\tfrac{b}{2})^2$ will blow some readers out of the water. Your observation of relationship between the terms is sufficient, and this bit can be deleted.

3) Next most important big thing is to organize the way you separate a = 1 from a not = 1. This separation is kind of buried three levels down the outline heirarchy, but it should be near the top. i.e., almost everything you have written becomes part of the a = 1 section, while the a not = 1 section either can be filled in with similar detail, or you can state the important results without deriving them carefully. This reorganization will take some care, but I'm confident you can do it.

#### Abram 6/17

Hi Tanya,

I actually like your overall approach to this page a lot. You clearly state the overall goal of completing the square, then go into a little bit more detail about what the tehnical steps will be, and then finally, fill it all in.

There are just a couple places where you don't quite connect the dots, and a couple other places where your language may be a bit too friendly or general.

First, the basics section. I agree with Gene about not boldfacing "Completing the square", maybe, but overall this section is great. Two big things and one small thing to change:

• "which cannot be solved for as is" doesn't have any meaning. Of course the equation can be solved -- you're about to show us how. Can you think of another way of getting across the idea you are after? I can give you some suggestions, but you can probably also come up with something.

Next, the PST section:

• I like that you are reminding readers that there's nothing particularly difficult about PST's. The phrasing "a big fancy word..." ends up sounding a bit condescending, and is a bit too conversational.
• Look for other places in this section or others where you are maybe a bit more conversational than really matches the tone of this site.
• "By completing the square, one of the components of the equation has to be a factored perfect square trinomial." This is a fantastic thing to tell the readers. Move it so it isn't buried under the "example" subheading. Also think of way to say a bit more precisely what you mean. You'll probably need more words to do this.

Steps for completing the square section:

• This section is fantastic.
• Combine steps 3 and 4 into a single step: just explain that you can see from the previous section that adding (b/2a)^2 to both sides of the equation will make the left side a PST.
• Drop step 6

The remaining sections:

• Having examples are great. I don't think you need quite that many.

Not quite right math. The following statements are either not quite true or don't use quite the terminology you are looking for. Let me know if you'd like help fixing them:

• It is not actually true that some quadratic expressions are not factorable. Any quadratic expression is factorable into (x+a)(x+b) if you allow a and b to be any complex numbers, not just integers. But you prob. can replace this statement with something informal that conveys the same basic message.
• In "relationship between terms" you say "numbers" when you mean "coefficients".

#### Gene 6/16

Want to have your first "quadratic equations" a mouseover which shows what it is? Some of your writing in the first paragraph is a bit rough. Maybe go over with your partner Rebekah? Both standard form and vertex form link to the parabola article, which is a bit confusing even though it has references to these forms. Perhaps say what they are in a mouseover and have "(see [Parabola article] for more detail)" or something.

Your first paragraph both begins and ends with something in boldface, although neither are defined! You actually show the procedure a bit later (and since this is also the title of the article I'd call it something like "Completing the Square Procedure" or something). The steps in it are all very small and rather than [showing] how 'bout mouseovers?

In general, you have some good material here but it's a bit confusingly presented. How about going over it with Kaitlyn? (and remember, she's just here for the rest of the week before she goes on vacation).