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Math Help - PDF on quadratic equations

  1. #1
    Super Member Bacterius's Avatar
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    PDF on quadratic equations

    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
    Attached Files Attached Files
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Bacterius View Post
    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
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  3. #3
    Super Member Bacterius's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    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 )
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  4. #4
    MHF Contributor
    Prove It's Avatar
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    At the bottom of page 4, where you have

    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

    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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  5. #5
    Senior Member roninpro's Avatar
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    Quote Originally Posted by Prove It View Post
    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.
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  6. #6
    Super Member Bacterius's Avatar
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    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
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  7. #7
    Super Member Bacterius's Avatar
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    Apologies for the update being so sluggish, I really can only work on it on week-ends
    Hopefully it will be finished by Sunday.
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  8. #8
    Senior Member apcalculus's Avatar
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    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?
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