Completing the ^2

Scary QuadraticsThere is no question that quadratic equations are one of the most difficult elements of Year 10 mathematics. Quadratic equations have many aspects of advanced algebra, and can seem to be completely useless mathematical constructions with no applications to the real world.

The truth is that, to an extent – this is true! Quadratics do have real world applications, but they are difficult to understand at first. Just like when you start riding a bike, you shouldn’t expect to be able to do a superman jump like one of the crusty demons of dirt!


But the most interesting thing about this video is not the great trick riding skills, but the fact that all of the riders when they are in flight, follow path of a parabola – the line of their trajectory can be described by a quadratic equation! Far from being completely unreal mathematical fripperies, quadratics are the simplest of the group of (non-linear) equations that model real world behaviour! While you are not expected to be able to use Quadratic equations to model things like this (yet!) it is important to know that all this hard work is actually useful!

This year you must master two skills – The General Solution to the Quadratic Equation and Completing the Square. There are other skills, of course, but these two things are the most difficult. First – completing the square (completing_the_square):

The general solution to the Quadratic Equation (G.S.Q.Eq – or Gee-squeak!) is another useful tool in your armory of techniques to solve equations. The problem is that the equation is somewhat complicated – and very difficult to remember – here is something that will help you to remember it – and make you wish you  could forget it!

See you in Class!

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30 Comments on “Completing the ^2”

  1. jessica b Says:

    oh my gosh there is so much stuff to remember in this unit
    I’m like full stressing out about the test tomorrow
    I’ve only just started to really get how to do all the completing the square stuff with the square roots

  2. Aashima singh Says:

    -sigh- since NO ONE is gonna get the ball rolling! yeah factorising is deffinetly the hardest thing we’ve covered this year, but i find it helps a lot if I make up a story to go with it. For example the G Squeak thing i make up someting like “b was feeling rather unhappy one day [-b] so he contemplated [+\-] rooting…” and so on:] i hope that was a sufficient coment cos im on my psp and my fingers are dying:] byye.

    ps- links to manuley rooting numbers?

  3. Mr G Says:

    Hi Jess,

    Yes, there is a lot to remember – it is one of the most difficult units on Year 10 Maths. One of the reasons it is so hard is that there don’t seem to be any “real” applications. Unlike trigonometry where you can see how it can be used, or even linear graphing where you can imagine how to use it – expanding and factorising just seems to be a lot of “tricks”.

  4. Mr G Says:

    Hi Aashima,

    The General solution to the Quadratic Equation is hard to remember – that’s one of the reasons I put the “Quadratic Song” up – in the youtube clip in this post. Once you’ve listened to it, you won’t have to try and remember the equation – you’ll wish you could forget it!

    Over Two Ay-ay, Over two ay-ay, Over two Ay-ay, OVER TWO AY!

  5. Matt Chung Says:

    isnt that related to linear equations
    that instead of squaring the number you
    cube the number instead making your line go in an arch
    because mr dimmeck said something about that last year
    but he didnt go into much detail because it was complicated
    mr g could you give me a brief idea of what sort of topics
    we would cover in unit 1/2 maths methods?

  6. stephen p Says:

    wow only the 3rd post. hey mr g. that formula that you showed us the other week about finding out the square root manually is pretty hard and confusing but if i got the hang of doing it then it might be ok.
    the factorising unit actually isnt the hardest thing we’ve done so far. i’m not sure if we’ve done it yet but indices is the bit i struggle in 😦
    im not sure if i’ve said enough yet, but i know of a different way to do long multiplication and for some people its actually easier, but i can’t explain it on this one blog. 🙂

  7. Tharanie Ratnakumar Says:

    hey mr G

    I’m feeling really confident about doing the Factorising test tomorrow. I have been working really hard and doing a lot of revision. I feel that this is the most comfortable i have been in a maths topic. I feel that this topic is a strength of mine. I just hope that shows in my test tomorrow. My only worry is making careless mistakes, looking at my previous test, that is my main problem in my test. I often rush in test as i get stressed out.

    Hopefully i can do good tomorrow


  8. lydia Says:

    i didnt know where to post this… and
    it has nothing to do with maths.. i think 🙂

    this is part one of six. about the world maybe ending in 2012.

    i dont think its true.. but see for yourself 🙂


  9. Jack Nichols Says:

    I am so relieved to have finally started a new topic in maths!!!!! Quadratic equations has definatley been the hardest topic this year and im so glad to have finished it. So far the work on modes, medians and means has been quite straightfoward and i am feeling very confident about it (it’s one of my better topics)


  10. Mr G Says:

    Hi Matt,

    Parabolas are related to linear equations – in more than one way! As you suggested, they are a higher power function, but squares not cubes. Cubics go in a wave pattern, not an arch.

    As to math methods, it starts with what we just finished, and goes into other types of lines (cubics, quartics, hyperbolas) and joy of joys, polynomial long division – it then goes back into probability and other fun stuff. You can find more details on

  11. Mr G Says:

    Hi Stephen,

    Here is a link to the manual square-root technique if you want to practice – understanding of this is important, particularly in the expertise you can develop in the algebraic underpinnings of the technique.

    ps. Indices are easy!

  12. Mr G Says:

    Hi Lydia,

    I’m a skeptic about these sort of things – there have been many predictions about the end of the world that have failed to come to pass. Thanks for sharing the link – it is amazing the things you find on the internet!

    Here is a criticism of the 2012 prophecies:

  13. Mr G Says:

    Hi Jack,

    Yeah, stats are really useful. As they say, there are three types of lies – Lies, Damn Lies & Statistics. If you don’t know how numbers can be manipulated, it is easy to be deceived…

  14. Anton Says:

    hey mr G
    Finally no more quadratics, i found that there was too much to remember, but im glad thats finished now, starting a new topic. All this medium mode and mean stuff im finding simple as its just a review of past years but this isnt my best topic because i dont really like statistics… But noooooo more QUARDRATICS !!!!!!! its something to be happy about

  15. brittney Says:

    hi mr G

    i have finished the stat wrok sheet up to the end of 10D
    so far i have been able to do all with little drama.
    i am happy that we have changed topics from quadratics, i am not looking forward to getting that test back.
    i know there is no way i did well. i forgot everything in that test.
    i should make up notes on that chapter later on before exams.
    thats about it.


  16. Mr G Says:

    Hi Anton,

    Sorry to tell you, but we will be doing quadratics again this semester – learning how to graph them and interpret them…

  17. Tina Says:

    hey mr G
    im glad that we’ve finished factorising and expanding
    the surprise of not having a calculator was a big shock but i’m pretty sure i did alright without it
    im glad we’re doing stats now cause i find it really easy and after doing a few hard topics i’m very happy to just relax with something easy

  18. georgie Says:

    so happy we started a new topic because i was so confused about the last one so i hope i did okay in my test even though i dont think i did hah.
    this new topic is easier fo sho 😀
    but it just takes to long to do stem and leaf plots gah 😦

  19. John Makree Says:

    G’day G-train

    I’m sad to see that we will be doing quadratics again. On a postive note we r doin stats. It does get boring cause u do all the stuff over and over again but still better then the other topics.

    Go the Hawks!!!

  20. ToM Says:

    Mr G, wats goin on?

    I rekon it sucked that we had to continue on with quadratics after the holidays and thats why im so happy to be starting a new topic. Statistics are so much easier with that class pad calculator, its awesome. Thanks for showing me how to use it.

  21. Han. Says:

    Why hello.
    Sorry this is late!!
    I didn’t really like quadratics. I understood them, but then I had trouble getting back onto them after the holidays. That sucked.
    But after the test, I think that I’ve learnt that if I do a lot of revision, I’ll be able to do the questions. 😀
    I’m quite happy with my result for the test, but I think I would’ve done better if we did it before the holidays.
    Anyway, one comment down. HAHA.
    By the way, that little ‘Captcha-type’ thing is really lame.. “bounceout57”!? Hmm..
    – Hannah.

  22. Hel Says:

    Hi mr G

    I think the quadratics test was one of the hardest tests ive ever done and it was a test which i felt i really needed a cheat sheet because id forgotten most of the formulas but actually it wasnt that id forgotten the formulas i think it was that i didnt know what equation you use a particular formula on if that makes sense.

    anyway i hope this topic is better.

  23. Jennifer Says:

    Hi Mr.G
    Sorry for the late entry.
    I got my test result back today and expected to get a low mark as in recent tests aswell.
    As you could already notice my maths is definatly not my strongest subject and probly the least subject i enjoy (sorry) but im trying! Like Tom i was abit angry that we had to continue quadratics after the holidays because to be honest i forgot most things but im alot more confident with statistics and i am doing my homework and writing notes with every chapter now and i bought a new book so im heading somewhere finally because with what i want to do i need to do maths so i better start focusing now.
    And thanks for showing me how to do statistics on the calculator .
    Anyway bye

  24. Stefanie Says:

    That incredibly annoying song on the quadratic formula surprisingly help me gain a mark in the test! Thanks,

  25. Liz Says:

    Ok i finally got onto this. Now for my entry. I found that the topic we just did, Quadratics was really hard and I didnt get it at all no matter how hard I tryed, I still tryed my best in the test. I am glad we have moved on to Statistics I feel confident already with this topic and i actually get how to do it.


  26. annoymous Says:

    a little advice from a yr 11 doing maths methods
    quadratics are hard at 1st( in fact i even know some people in yr 11 who still struggle on them) but like all maths equations:


    the more you do them, the more you’ll become skilled at it.

    dw in time you’ll understand and get it, all you need to do, is practice practice practice!

  27. Jack Says:

    Hey sir! is there any practice tests online for monday’s test?


  28. Rachel Says:

    hey mr g
    I was just on maths online doing the Quadratic work and in the demonstration there was 3 dots in the shape of a triangle at the begining of the answer and i was just wondering what that symble ment.

  29. […] ps. Another (older) post by me about quadratics and completing the square is at this link […]

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