# Quadratic Graphs

'Help the firefighter put out the fire by describing the correct path of the water'

This activity is all about describing parabolas or quadratic graphs. In the final games you will need to help the firefighter in his mission to put out the fires by entering the correct equation of the water path. If the firefighter gets the path of water right he puts the fire out, if not the fire keeps on raging. To help him on his mission you will need to learn about the properties of these graphs. Don't worry, this activity will guide you through from start to finish, although you should have done some work on factorising quadratics beforehand.

### The Hook

This is not related to firefighting, although this daredevil is quite brave. Watch the following video (this is not a spoof, it is real!).

Can you describe the shape of the path that the human cannonball follows?

To land on the net the man has to calculate the correct trajectory, otherwise SPLAT! broken back. He needs to work out the right angle so that he flies on the right parabola. The following activity will help you describe these sort of parabolic paths.

### How to use this Activity

Watch this 3 minute video to get an overview of the activity

### Investigation 1

Click on the following to open up the full instructions to complete the first part of the investigation to explain the symmetry of the graphs. You will need graphing software to complete the first part of this investigation. Geogebra can be downloaded or used online.

#### Copy My Graph 1

Click through all the questions and make 'your curve' lie on op of the dotted curves by entering the correct equation in the input box at the bottom. Put your answers on the worksheet downloaded from above.

### Completing the Square

• Using the graph below, grab the curve and move it around.
• What happens to the equation?
• Predict the new equation before you move it?
• Once you have understood what is going on go to Copy My Graph 2 and make each of the graphs.
• Put your answers on the worksheet downloaded from above.

### Investigation 2

Click on the following to open up the full instructions to complete the second part of the investigation.

### Firefighter Games

Once you have completed the investigation above you are ready to play the Fireman Sam games.“Quick! Put out the fire! Enter the correct equation so that Sam stands by the hosepipe and he aims at the fire.”

Hint - You may find entering the equations in the factorised form from above helpful!

### Extension - Angry Birds

If you enjoyed this activity and need a challenge try Angry Birds!

You are the chosen one! Are you ready for Angry Birds Star Wars? In this game you will need to enter the 'Pork Side'. Harness 'The Force' and your supernatural powers to help Luke Skywalker and Chewbacca correctly aim their path and eliminate the evil pigs. You will quickly realise that space travel takes parabolic paths so any knowledge that you have gained about quadratic graphs will stand you in good stead. Take care, Young Jedi, to use 'The Force' for good.

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