# 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?

### Syllabus links

Quadratic Functions and their properties.

* 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
- 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 jamesn@inthinking.co.uk In time some of these twists may appear here....

## Comments 4

Veronica Diaz1 November 2017 - 15:00Hi I have opened this on two separate pages now and it is still not working. This page is blank for me, with the exception of the titles of the sections and the wording after. All the embedded material is white space.

Jim Noble8 November 2017 - 16:36Hi Veronica. Thanks for letting me know and sorry for inconvenience. In any case I have re embedded all the videos now. Although, I now hear the tinny soundtracks so wil put it on my list to re make these. Thanks, Jim

Dulce Macalino5 June 2018 - 04:26Hi. i am interested learning and making the dancing quadratics, im figuring out. can you help me? thanks.

Jim Noble6 June 2018 - 14:14Hi Dulce - Sure - I don't know what tech platform you are using - I recommend using desmos, if you enter a function in terms of a variable then you will be asked if you want the variable to be a slider so you can dynamically change the value of that variable. Think about using the completed square form of a quadratic and using the variable more than once..... let me know how you get on....

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