PDF on quadratic equations

Nov 2009
927
260
Wellington
Hello,
I've been writing a paper going through quadratic equations (algebra and graphing), and I intent to ask a moderator to review and sticky it if appropriate in the Pre-Algebra section of MHF. I feel it might be useful to a whole bunch of people, probably infinitely many xD. But first, I am looking for peer review, so I provide the first version of my paper for you all to read. The paper is attached to the thread.

The PDF does not expect you to be a layman and does require some basic skills at algebra and some notions of graphs (nothing very difficult though). I will accept any constructive critics and tips on how to present ideas fluently, or format the paper so as to make it as clear and enjoyable to read as possible. There is (hopefully) going to be a reviewed version based on your opinion, maybe adding some more stuff into it and correcting some flaws that I might have missed.

Thank you all :)
 

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CaptainBlack

MHF Hall of Fame
Nov 2005
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Hello,
I've been writing a paper going through quadratic equations (algebra and graphing), and I intent to ask a moderator to review and sticky it if appropriate in the Pre-Algebra section of MHF. I feel it might be useful to a whole bunch of people, probably infinitely many xD. But first, I am looking for peer review, so I provide the first version of my paper for you all to read. The paper is attached to the thread.

The PDF does not expect you to be a layman and does require some basic skills at algebra and some notions of graphs (nothing very difficult though). I will accept any constructive critics and tips on how to present ideas fluently, or format the paper so as to make it as clear and enjoyable to read as possible. There is (hopefully) going to be a reviewed version based on your opinion, maybe adding some more stuff into it and correcting some flaws that I might have missed.

Thank you all :)
In section 2.2 in the list of methods of solving quadratics you should have completing the square as this is often taugt befor the quadratic formula.

In the bit about factorization there is no mention of the rational roots theorem.

In the derivation of the quadratic formula you provide no words telling the reader what you are doing.

CB
 
Nov 2009
927
260
Wellington
In section 2.2 in the list of methods of solving quadratics you should have completing the square as this is often taugt befor the quadratic formula.

In the bit about factorization there is no mention of the rational roots theorem.

In the derivation of the quadratic formula you provide no words telling the reader what you are doing.

CB
Thank you Captain Black for your comments,
I will take them into account for the rewriting of the paper (well not exactly rewriting, "update" would suit better :))
 

Prove It

MHF Helper
Aug 2008
12,883
4,999
At the bottom of page 4, where you have

\(\displaystyle ax^2 + bx + c = \left(x - \frac{-b - \sqrt{b^2 - 4ac}}{2a}\right)\left(x + \frac{-b + \sqrt{b^2 - 4ac}}{2a}\right) = 0\)

should actually read

\(\displaystyle ax^2 + bx + c = a\left(x - \frac{-b - \sqrt{b^2 - 4ac}}{2a}\right)\left(x + \frac{-b + \sqrt{b^2 - 4ac}}{2a}\right) = 0\).


You don't factorise equations, you factorise expressions which happen to be on one side of the equation.


You should give more examples and exercises for everything you are trying to teach.


You haven't explained how to factorise non-monic quadratics - the method where you break the middle term and factorise by grouping is the best.


Except for one sentence in the introduction, you have not given any real world applications.
 
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Nov 2009
485
184
Except for one sentence in the introduction, you have not given any real world applications.
I wonder: are there really any honest and direct real-world applications of the quadratic formula? Many math textbooks give improbable and contrived "word problems" as their application, and in my opinion, it does more damage than good.

Maybe it is better to leave it out, if nothing sensible can be found.
 
Nov 2009
927
260
Wellington
Of course ! The only example I actually gave in my PDF (at this point, it's currently being updated) about projectile motion is fundamental.

But indeed, usually, math textbooks do give stupid problems that lead to thinking that the QF is useless. But it's not ! :)

Ooh I need to get some communication skills asap xD
 
Nov 2009
927
260
Wellington
Apologies for the update being so sluggish, I really can only work on it on week-ends :(
Hopefully it will be finished by Sunday.
 
Apr 2009
293
94
Boston
This looks very neat. Thanks for sharing. May i ask what type of utility you used to create the graphs?

On a more general note, anybody recommend a good resource/tutorial for authoring with LaTeX for beginners?