Theta Mathematics Workbook (NCEA L2)© Pearson Education New Zealand 2005

x

y16

16.09

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. xy 2

2)4( xy

4

Theta Mathematics Workbook (NCEA L2)© Pearson Education New Zealand 2005

x

y16

4

16.09

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.

Theta Mathematics Workbook (NCEA L2)© Pearson Education New Zealand 2005

x

y16

4

16.09

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.

xx 2)4( 2

xxx 21682

016102 xx

0)8)(2( xx

8or 2 xx2 8

Theta Mathematics Workbook (NCEA L2)© Pearson Education New Zealand 2005

x

y16

4

16.09

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.

2 8

The area shadedis the area under the parabola.

The combination of bothis 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.

Theta Mathematics Workbook (NCEA L2)© Pearson Education New Zealand 2005

x

y16

4

16.09

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.

Area

2 8

3216

38

1282563

512)464(

dxx8

22

8

2

2 )168( dxxx

Under line Under parabola

3216128256

3504

60

1443

50460

14416860

8

2

23

1643

xx

x 822x

units. square36