## 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.

**Explore posts in the same categories:**Mathematics

November 14, 2010 at 4:58 PM

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

November 14, 2010 at 7:06 PM

Hi Jack,

I’m glad the video helped. I’ve fixed the playlist so try again and look at those videos.

Have you found any useful resources?

November 14, 2010 at 7:24 PM

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

November 15, 2010 at 4:47 PM

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.

November 15, 2010 at 8:38 PM

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

abovethe 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

onthe 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

belowthe 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…

November 18, 2010 at 3:18 PM

Thank you for that link! Interesting how they portray it with the GSQep to show its function 🙂

November 15, 2010 at 8:18 PM

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.

November 16, 2010 at 7:47 PM

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.

November 17, 2010 at 6:06 PM

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

November 17, 2010 at 7:10 PM

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..

November 17, 2010 at 9:40 PM

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.

November 18, 2010 at 7:03 PM

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.

November 20, 2010 at 9:32 AM

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 🙂