PRESENTATION MATHS 2( NOT EDITED)

QUESTION 3

The figure above shows a quadratic curve and a straight line with respective equations.
= 2 + 2 + 2 and 7 − 2

The points A and B are the points of interaction between the quadratic curve and the straight line.
a) Find the coordinates of A and B.
b) Determine the exact area of the finite region bounded by the quadratic curve and the
straight line, shown shaded in the above figure.

a) = 2 + 2 + 2 = 7 − 2

= 2 + 2 + 2 = 7 − 2

= 2 + 2 − 7 + 2 + 2 = 0

= 2 − 5 + 4 = 0

( − 4), ( − 1)

= 1, = 4

A, = 7(1) − 2 , = 7(4) − 2

= 5 = 26

= (1, 5), = (4, 26)

b) 1 = (26 + 5) × 3 × 1

2

=46.5

4

2 = ∫ 2 + 2 + 2

1

=( 3 + 2 2 + 2 )14
3 2

= ( 3 + 2 + 2 )14
3

=[ 43 +42 + 2(4)] – [13 +12 + 2(1)]

33

= 42

Shaded Area = 93 − 42

2

= 4.5