You have been looking at some graphs with equations of the form y = mx (since c is zero).
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1 Spreadsheet graphs for Ecel 2007 In this activit ou will use a spreadsheet with the etension.ls to eplore how the shape and the position of a graph changes when ou change the constants (the fied values) in its equation. You will look for connections between the numbers in equations like = 2 + 3, = 20/ and = and the graphs that represent them. Information sheet A Using Spreadsheet graphs Open Spreadsheet Graphs.ls The first sheet is shown below. It will show graphs with equations of the form = m + c At present the values of m and c are both zero. You can change these values using the scroll bars. Leave the value of c equal to zero, and use the scroll bar to change the value of m. Tr using different parts of the scroll bar to see what happens and look at the tables and graphs ou get. scroll bars You have been looking at some graphs with equations of the form = m (since c is zero). Nuffield Free-Standing Mathematics Activit Spreadsheet graphs.ls Student sheets for Ecel 2007 Copiable page 1 of 5
2 B Eploring graphs with equations of the form = m Keep c = 0, so that in each case is proportional to. Tr these 1 What point on the graph does the line alwas pass through? 2 What happens to the line as the value of m increases from 0 to 5? 3 What happens to the line as the value of m decreases from 0 to 5? C Eploring graphs with equations of the form = c Now keep m = 0 and use the scroll bar to change the value of c. Tr these 4 What happens to the line as the value of c increases from 4 to 4? D Eploring graphs with equations of the form = m + c Tr these Keep m = 1 and use the scroll bar to change the value of c. 5 What happens to the line as the value of c increases from 4 to 4? Keep m = 1 and change the value of c. 6 What happens to the line as the value of c increases from 4 to 4? Reflect on our work What can ou sa about the link between the line and the value of c? What can ou sa about the link between the line and the value of m? Can ou think of an real life situations that can be modelled b an equation of the form = m + c? Nuffield Free-Standing Mathematics Activit Spreadsheet graphs.ls Student sheets for Ecel 2007 Copiable page 2 of 5
3 E Eploring graphs with equations of the form = k/ Now look at the second sheet ( = k over ). It will show graphs with equations of the form Eperiment with different values of k. k 7 On the left-hand set of aes, below sketch the graph when k is positive. 8 On the right-hand set of aes, sketch the graph when k is negative. 9 What point on the graph does the curve never pass through?. F Eploring graphs with equations of the form = a 2 + b + c Now look at the third sheet. It will show graphs with equations of the form = a 2 + b + c. Questions 10 to 13 are about curves with equations of the form = a 2 Keep b and c at zero and eperiment with different values of a. 10 On this set of aes sketch the graph when a is positive. 11 Describe what happens to the curve as the value of a increases from 0 to 5. Nuffield Free-Standing Mathematics Activit Spreadsheet graphs.ls Student sheets for Ecel 2007 Copiable page 3 of 5
4 12 On this set of aes, sketch the graph when a is negative. 13 Describe what happens to the curve as the value of a decreases from 0 to 5. Questions 14 to 16 are about curves with equations of the form = a 2 + c Keep a = 1 and b = 0. Use the scroll bar to change the value of c. 14 What happens to the curve as the value of c increases from 4 to 4? Keep a = 1 and b = 0. Change the value of c. 15 What happens to the curve as the value of c increases from 4 to 4? Tr other values of a and c, keeping b = What can ou sa about the link between the curve and the values of a and c? Questions 17 to 21 are about curves with equations of the form a 2 b Keep a = 1 and c = 0 and change the value of b. 17 Describe what happens to the curve as the value of b increases from 0 to 4 Write down anthing ou notice. Nuffield Free-Standing Mathematics Activit Spreadsheet graphs.ls Student sheets for Ecel 2007 Copiable page 4 of 5
5 18 Describe what happens to the curve as the value of b decreases from 0 to 4. Now keep a = 1 and c = 0, and change the value of b. 19 Describe what happens to the curve as the value of b increases from 0 to 4. Write down anthing ou notice. 20 Describe what happens to the curve as the value of b decreases from 0 to 4. Eperiment with different values of a, b and c. Check what effect changing each constant has on curves with equations of the form = a 2 + b + c. Reflect on our work Describe the effects on the graph of changing each constant, a, b and c in the equation = a 2 + b + c. Nuffield Free-Standing Mathematics Activit Spreadsheet graphs.ls Student sheets for Ecel 2007 Copiable page 5 of 5
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