Tag: quadratics

Stacks of Quadratics

Firstly I would urge you to try the question in the photo yourself. It requires some knowledge of powers and solving quadratics and is wonderfully satisfying to find all SIX solutions.

Looking at easier examples

Questions like this are a great example of finding creative ways to practice fundamental skills. In this case one of the key skills being practised here is the ability to solve quadratic equations and rearranging them into a form that you can solve easily. So how to introduce this to a class?

Lets look at the example in the picture – How can we can get to a solution of 1 on the LHS of our equation? The two cases that make this happen: Case 1 by setting (x-1) = 1 and case 2 by setting (x-1) = -1

Both these methods when squared will give us our answer of 1 and so that is where we will get our final values of x to be 2 and 0.

So taking it a step further we now an expression as our power which gives us a third case: Setting x+2 to zero. When the power is zero whatever is inside the bracket is irrelevant as any real numbers to the power of zero equal to 1.

Okay 1 to the power of anything is one so x-1 = 1 gives us our first solution: x=2

In case two we need -1 to an even power to get to one so we have x-1 = -1 which gives us a solution of x=0 which when put into the power gives us an even power so it must be a solution

Finally in case 3 we set x+2 = 0 which gives us our third solution and final solution which is x=-2 and it is solved! Now can we use this simpler example to work our way up to the six solutions of the first problem?

Creative Practice

I used the sheet above as a starter in my first lesson with my new year 11s – as a little bit of a fun way to gauge both their ability and their desire to apply maths they definitely know in ways they might not have seen before. The questions don’t lead onto each other as nicely as I might like but once we had discussed the first few the whole class were able to get their teeth into the rest of them.

By working through this small exercise they were able to practise factorising and solving quadratics in a way that felt fresh and interesting whilst also giving me an opportunity to circulate and learn more about my class.

Post Credits

I will not explain the full explanation for the question as it seems only fair to direct you to the original video here for a lovely detailed work through of the solution. Once you have watched the video try the rest of the worksheet!

I encourage you to try each of the questions looking at each of the three cases. Then try and come up with some of your own that fit this format – I always think one of the best ways to improve is to play around with writing your own questions and these are a fun way to start!

If you want to download the worksheet as a word document click here

Answers can be found on our Resources page

Thanks for reading!

NJK