Unit 11


Topics covered within this unit: 11.1 Non-linear patterns – quadratic 11.2 Quadratic functions 11.3 Quadratic functions in real life


The Learning Outcomes covered in this unit are contained in the following sections:


AF.1a AF.1b AF.1c AF.2c AF.7a AF.7b AF.7c AF.7d


Key words Second diff erence


Quadratic pattern Non-linear pattern Minimum point Maximum point Quadratic function Parabola


Non-linear patterns and functions – quadratic


Something to think about …


The table shows the heights of a football at various times after a footballer kicks the ball to a team-mate from a podium.


Time (sec)


Height (metres)


1. 0 0·25 0·5 0·75 1 1·25 1·5 1·75 2 2·25 2·5 6 15 22 27 30 31 30 27 22 15 6


If you were to graph the height of the ball against time, do you think this would be a linear graph?


Give a reason for your answer.


2. If not, what shape do you think the graph would be?


Give a reason for your answer.


3. Draw a sketch of the graph of the height (y-axis) of the ball against time (x-axis).


4. What height above the ground is the podium? 11.1 Non-linear patterns – quadratic


By the end of this section you should be able to: ● identify a quadratic pattern ● compare and recognise diff erent types of patterns


In Unit 2 of this book, we learned that a linear pattern is when the fi rst diff erence (the diff erence between the terms) is constant and when a linear pattern is graphed it forms a straight line.


An example of a linear pattern is 5, 8, 11, 14, 17. The fi rst diff erence in this linear pattern is +3.


T1 First diff erence


T2 First diff erence


T3 First diff erence


T4 First diff erence


T5


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Linking Thinking 2


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