## Quixotic Quadratic Queries Qause Qonfusion

Welcome to Mathematical Methods – a subject which will prepare you for using mathematics to analyse the world and introduce the concept of developing theoretical models to investigate potential results of decisions. It is also a subject that will require you to work **hard **to master the skills and techniques so that you can use them effectively.

We have already completed the simplest work of the year, revising skills which you should be familiar with from previous years of mathematics – simple linear equations, systems of functions and basic coordinate geometry. Now, we start to go further, by investigating non-linear relationships – that means all lines that can be drawn on a graph that are not straight. The simplest of these are the quadratics – which have the shape of a smile (or a frown), just like the one in graph just above.

You will have studied this last year, and you may have become quite good at factorising and sketching quadratics – which is good. If you are not so confident, you will have time to revise, but you will have to put in additional work. We will be going a lot further with quadratics over the next month, and you will need to be prepared!

So, first let’s define a quadratic. You may remember we defined a polynomial in class recently, as an expression where each term contains a positive integer power of a pronumeral. You can see the sort of expressions which are not polynomials in the picture to the right. A quadratic is a particular type of pronumeral, where the highest power is “2” – in other words, it has an “x²” term in the expression, and nothing higher.

You’ll need to be able to do many algebraic operations on quadratic equations, but the first thing is converting between the three different forms of any quadratic equation. The first form is the so called “standard form”, which has the form of “y = ax² + bx + c”. This form is the most useless – the only information you can get is the y-intercept (from the “c” constant) and the general shape (from the “a” constant). You can see more about the effects of these constants at this link.

The second form is the factorised form, in which you see the expression rewritten and re-organised in brackets, i.e. “y = a(x + b)(x + c). Note that the values a a,b & c are not the same in any of the forms, except by coincidence. From the factorised form, you can use the null-factor law to determine the x-intercepts of the graph of the equation. Note that it may be possible that a particular quadratic function does not have a factorised form (if the graph does not have x-intercepts!).

The third and final form is called either the “vertex form” or “turning – point form), and has the following general appearance: y = a(x + b)² + c, and as you might guess by it’s name, it gives you the coordinates of the turning point of the graph. You can get to the vertex form by completing the square on the standard form.

Here is a video that covers the same theme, but with a voice-over explanation:

Finally, here are three documents that may help you:

1. Factoring Flowchart (link)

2. Quadratic Notes (link)

3. Advanced Notes (link)

And also checklist for chapter two (link).

Now, it’s your turn. Share a resource that you have found – on the internet, or anywhere else – that you have found useful so far this year – and an explanation of why you have found it useful. *Everyone* in the class must share a resource. If you find a resource that someone else posts useful – say so!

See you in class!

**Explore posts in the same categories:**Algebra, Mathematics, Year 11

February 26, 2013 at 10:46 AM

i found this on khan academy, all about quadratics. i found it quite useful

https://www.khanacademy.org/math/algebra/quadratics/

February 26, 2013 at 10:53 AM

Thats alot of vidoes 😛

February 26, 2013 at 10:50 AM

Kyle here, this page helps 🙂 http://www.mathsisfun.com/algebra/polynomials.html

😀 😀

February 28, 2013 at 7:37 PM

Indeed, Kyle. Maths is Fun – but sometimes it is also hard work!

February 26, 2013 at 10:55 AM

Hello there, I was having a great deal of trouble with polynomial long division, and I am still having some trouble but this has helped a bit.

http://www.mathsisfun.com/algebra/polynomials-division-long.html

Hope this helps :I

February 28, 2013 at 7:40 PM

Hi Sam,

Going deep here – you need to make sure you are in full command of chapter 2 before you go for chapter 3.

February 26, 2013 at 7:50 PM

I found this on purple math and it’s useful for this chapter (Quadratic) that we are doing, hope this might help 🙂

http://www.purplemath.com/modules/solvquad.htm

February 26, 2013 at 9:53 PM

Excellent find, Ngun. PurpleMath is one of my favourite sites. Every should look through it regularly.

February 27, 2013 at 4:01 PM

For quadratic chapter, I think it’s gonna be useful and helpful for us…..!

February 27, 2013 at 4:07 PM

For quadratic problems, hope this web links will be helpful for us. It’s simple and easy to understand. 😉

February 27, 2013 at 4:16 PM

Hope it’s useful and helpful for us 😉

February 27, 2013 at 4:18 PM

Hope this link is useful and helpful for us 😉 http://www.mathsisfun.com/algebra/polynomials-division-long.html

February 27, 2013 at 5:39 PM

Hi Lian,

Everyone wants to get into PLD! Just wait until we get to synthetic division..,

February 27, 2013 at 6:03 PM

http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/Example%201:%20Solving%20a%20quadratic%20equation%20by%20factoring

February 27, 2013 at 7:23 PM

Hi Megan,

Good choice of resource – but remember you should be saying what it is you like about the resource you post.

February 27, 2013 at 9:21 PM

as much as this link has already been used a million times as far as i can tell it is still the video that has helped me the most.

https://www.khanacademy.org/math/algebra/quadratics

February 28, 2013 at 7:04 AM

I understand what we are doing at the moment…

I like the wolfram site, pretty technical but for some weird reason I like reading it. I hope this helps.

http://mathworld.wolfram.com/Polynomial.html

February 28, 2013 at 7:36 PM

Hi Luke,

Be careful with Wolfram – you’re right, it is *very* advanced, and may take you beyond what you need to master. While extension is good, you need to make sure you can score 90%+ on the assessed materials before going to far…

March 11, 2013 at 8:18 PM

hey Sir it’s me Arina! i think i wont be able to finish the book check on time! can you please just give me alittle more time? thank-you.

oh and by the way can i get you email aswel?…mine is arinanop@hotmail.com

March 16, 2013 at 7:49 PM

hey mr g, i have a few problems with the math work, after this migraine that i had my eyes cant seem to focus on anything properly and as i am still getting over this migraine, concentrating hard on things just gives me a headache, there is also the problem that i cant understand quite a bit of it