'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

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.

#### 'Curve Dancing'

New - Section 6.3

Previous - Section 4.3

### 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