Dancing Quadratics
'Call the dancing! Get these quadratics in order and make them dance the way they should!'
Watch the videos below and work out what features of the functions involved are changing to make them 'dance' as they do. Understanding what moves a function is at the heart of understanding the function itself and that is the challenge in this activity. Of course the videos below are just the start. If part or all of these can be created then the next challenge is to think about what other dances can be choreographed!
Aims
The aim here is to explore the properties that transform quadratic functions so that the shifts can be understood and recognised.
Resources
Students will need access to computers for this activity and also access to this page so that they can see the videos and try to recreate them.
Dancing Quadratics
Get a flavour for the task ahead. This video was made by entering 8 different quadratic functions all sharing 1 dynamic constant that was then varied.
'Wave em'
How was this video made? What constant is varying? Can you make a similar video?
'Line Dancing'
How was this video made? What constant is varying? Can you make a similar video?
'Curve Dancing'
How was this video made? What constant is varying? Can you make a similar video?
Description
Here follows an outline of what the task is. If students are not reading this page then the teacher will need to show and give this overview.
- watch the videos starting with 'Wave em like you just don't care'
- using a graphing package try to plot a quadratic function that includes at least one 'dynamic variable'
- by changing the dynamic variable, try to recreate the 'dance' in the video
- make a statement of conclusion about the effect of varying the constant
- repeat the exercise with the other videos
- ask and try to answer related questions about 'How would you....' included in the worksheet
- if screen capture software is available make the ultimate 'dancing quadratics video'
I did it my way!
As a practising maths teacher I know that most of us like to give activities our own little twist and do them 'our way'. It would be great to add a little collect of 'twists' from users. You can either add your twist to the comments section below or e-mail them directly to me at [email protected] In time some of these twists may appear here....