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Theta Mathematics Workbook (NCEA L2) © Pearson Education New Zealand 2005 x y Draw the graphs of the line y = 2x and the parabola given by y = (x – 4) 2 on the same diagram. Calculate the area enclosed by the line and the parabola. Draw the graphs. xy2 2 )4( xy 4

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Theta Mathematics Workbook (NCEA L2) © Pearson Education New Zealand 2005 x y Draw the graphs of the line y = 2x and the parabola given by y = (x – 4) 2 on the same diagram. Calculate the area enclosed by the line and the parabola. To find the area between the line and the parabola, we first need to find the x-values of the points of intersection. Solve the equations y = 2x and y = (x – 4) 2 simultaneously.

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Theta Mathematics Workbook (NCEA L2) © Pearson Education New Zealand 2005 x y Draw the graphs of the line y = 2x and the parabola given by y = (x – 4) 2 on the same diagram. Calculate the area enclosed by the line and the parabola. To find the area between the line and the parabola, we first need to find the x-values of the points of intersection. 28

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Theta Mathematics Workbook (NCEA L2) © Pearson Education New Zealand 2005 x y Draw the graphs of the line y = 2x and the parabola given by y = (x – 4) 2 on the same diagram. Calculate the area enclosed by the line and the parabola. 28 The area shaded is the area under the parabola. The combination of both is the area under the line. The required area is shaded Look at the areas shaded on the graph. Thus the required area is the difference between the area under the line between x = 2 and x = 8 and the area under the parabola.

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Theta Mathematics Workbook (NCEA L2) © Pearson Education New Zealand 2005 x y Draw the graphs of the line y = 2x and the parabola given by y = (x – 4) 2 on the same diagram. Calculate the area enclosed by the line and the parabola. 28 Under lineUnder parabola

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