Mathematics: More than meets the eye!

The recent Transformers movies are some of the worst movies every made. They have nonsensical “plots”, direction that would ashame a moronic chimpanzee, and acting that would be boo-ed off the stage at a primary school.

Sort of appropriate then, that the nasty bit of algebra so far this year has the same name. I’m talking about Quadratic Transformations. We have already done the hard parts so far this year – you know how to complete the square, and you’ve practiced factorising until you are sick to death of it! You know the general solution to the quadratic equation formula (GSQEq – “G-Squeak”). Now we have to look at the discriminant:

But what are a, b and c? In the standard form of the quadratic equation, they are, respectively, the coefficients of the x squared term (a), the x term (b) and the constant (c). When you put these values into the discriminant formula (above), it tells you how many x-intercepts (sometimes called “roots” or “zeroes”) that particular quadratic expression has.

If the value of the discriminant is positive ( > 0), there will be two intercepts. If it is equal to zero, it will have one intercept. If it is less than zero, there will be no intercepts, as shown in the diagram above.

Here is a video – it’s not quite as bad as the latest transformers, but it is horrific in it’s own way:

Here are a sequence of videos that go into more detail; I recommend you check out the playlist, and decide which ones you need to watch.

Some links that may help you get your head around the concept (1, 2, 3, 4).

Remember that you must comment on posts if you want a good result for your ICT component.

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

See you in class.

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13 Comments on “Mathematics: More than meets the eye!”

  1. Jack Says:

    Hello sir, I found the links 2 and 3 helpful. 1 however is simple yet for some reason new for me. Link 4 is good because it helped me revise on the g-squeek. the Video attached is very humorous and easy to understand.
    However, the playlist cant be found :\

  2. CyberChalky Says:

    Hi All,

    This is another resource; I’ve put it in the comments to see who is reading the comments and who isn’t…

    Here is a resource that will let you experiment with transformation of parabolas – read the instruction and play with it. There will be questions like this on the exam!

    http://seeingmath.concord.org/Interactive_docs/QT_UsersGuide.htm

  3. Jordan Says:

    Hey sir, the dancing in the vid is terrible. But i looked at the diagram and i was really confused and didnt really understand it.

    • CyberChalky Says:

      Hi Jordan,

      I guess you are talking about the diagram which shows the different parabolas. What that diagram is showing you is the number of x – intercepts a parabola can have. A parabola can have:
      No (0) x-intecepts (the green parabola) – this means the turning point of a (positive) parabola is above the x-axis. You can see that the parabola doesn’t touch the x-axis.
      One (1) x-intercept (the purple parabola) – this means that the turning point of a (positive) parabola is on the x-axis. You can see that the parabola just touches the x-axis. It sort of looks like it bounces off the x-axis, and the turning point and the x-intercept have the same coordinates.
      Two (2) x-intercepts (the blue parabola) – this means that the turning point of a (positive) parabola is below the x-axis. The parabola passes through the x-axis, and then comes back up through again.

      Each of the graphs has a symbol on it, a triangle (Δ). This is the symbol for the discriminant, which is part of the general solution to the queadratic equation (GSQEq – G squeak). The discriminant determines how many intercepts there are. If Δ>0, then two intercepts. If Δ=0, then one intercept. If Δ<0, then no intercepts.

      Here is a link that may help. Tell me if this has helped you understand.

      As to the dancing in the video, It’s better than me doing it…

  4. Brendan Says:

    I found the second and third links the most helpful, they just covered stuff that I needed to revise on and the aerobics video…… well I’ll go strange at the least.

  5. Jordan Says:

    Hey sir, i found the link abit helpful but i probably need to practise it in class more to get a better understanding of it. As i am still not 100 percent.

  6. Jason Says:

    the links were very helpful and im prity confident with parabolas now.

  7. Muhammad Says:

    I found the first link very helpful, but still little confused with it. I couldn’t watch the videos because it takes too long to load, but eventually watch it some day..

  8. Stephanie Says:

    The link that you provided was useful because it shows the steps on this topic but i was still a bit confused in some areas.

  9. Michelle Says:

    The video was disturbing, but the links were quite helpful, links 3,4 were good…then again, so were the others. I think i still need to keep revising.

  10. Bianca Says:

    Hi sir,
    the video was quite ridiculous, but entertaining.
    I still dont understand the concept but hopefully using the links you provided and going over maths online work will help.
    Thanks 🙂


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