Page 17 - Focus SPM KSSM Tg 4.5 - Add Maths

Additional Mathematics SPM Chapter 2 Quadratic Functions

For the case of a . 0: For the case of a  0:
When the value of b changes, the position of When the value of b changes, the position of
vertex vertex
• will be shifted to the left when b . 0. • will be shifted to the right when b . 0.
• will be shifted to the right when b  0. • will be shifted to the left when b  0.
SPM Tips

• The larger the value of |b |, the further the position of vertex is displaced from the y-axis.
• When b = 0, the vertex is on the y-axis.
• When the same value of b changes sign from positive to negative or from negative to
positive, the position of the graph is reflected on the y-axis.

Moves f(x) f(x)
upwards Moves upwards
Form 4
when c > 0 c > 0
c > 0 when
c = 0 c > 0 x
0
x Moves c = 0
Moves 0 downwards
Only the downwards c < 0 when c < 0
c < 0
when
value of c c < 0
changes When the value of c changes, the shape of the graph is unchanged but the position of the graph
• will be shifted vertically upwards when c . 0.
• will be shifted vertically downwards when c  0.
SPM Tips The effects of the
changes in a, b
and c on the graph
c is the value of the y-intercept. INFO

The y-intercept does not change.
14 f(x)
f(x) = x + 2x + 2
2
The diagram below shows the sketch of the graph of
f(x) = x + 2x + 2. Make generalisations on the shape
2
and position of the graph of the given functions when 1 2
—
2
compared to the values of a, b and c for the following f(x) = x + 2x + 2 x
2
functions. Hence, sketch the graphs of the functions. 0
1 (b) f(x) = x – 2x + 2
2
(a) f(x) = x + 2x + 2
2
2 When the value of b changes from +2 to –2, the
(b) f(x) = x – 2x + 2 position of the graph reflects on the y-axis.
2
(c) f(x) = x + 2x – 1 The shape and y-intercept do not change.
2
f(x)
f(x)
2
f(x) = x + 2x + 2 f(x) = x + 2x + 2 f(x) = x – 2x + 2
2
2
2
2
x
0 x
0
Solution
1
2
(a) f(x) = x + 2x + 2 (c) f(x) = x + 2x – 1
2
2 1 When the value of c changes from +2 to –1, the
When the value of a changes from 1 to , the position of the graph is shifted vertically. The
2
width of the graph increases. y-intercept is –1. The shape of the graph does not
change.
40