And you thought Quadratics were bad…

So, we’ve gone through two and a bit chapters of Mathematical methods so far, and you are beginning to think that you’ve done the worst of it – it can’t get that much harder, can it? Really?

Well, welcome to cubics, quartics and higher order polynomials – they are the big brothers and sisters to the humble quadratic, and they’d like to have a word with you about beating up on their sibling, the poor little quadratic – something about “completing your square”

On a more serious note, if you are feeling alright about algebra so far, the next section isn’t any harder – just a few more ideas – nothing new or harder than we’ve done so far, just more. Just like when we started quadratics, the first thing we do with cubics and quartics  is to identify the common pattern, and be able to factorise them directly from recognising that pattern.

Once we can do that, we will look at how you can start to graph these functions from their intercepts – but that means we need a way of finding all the intercepts. We already knew from our studies of the Null Factor Law (NFL) that the factors of a quadratic equation can give the intercept. The Remainder theorem (right now, that irritating chorus should be going through your head) allows us to find the factors by finding values for a where f(a) = 0 for a given f(x). Combining all this knowledge gives us the ability to sketch almost any graph!

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!