Completing the ^2

There 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!

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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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