Page 16 - Ranger SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 2 Quadratic Functions

Solution Solution
1
(a) When a changes from 1 to , the width (a) When b changes from 2 to –2, the
2 vertex is to the left of the y-axis. The
of the graph increases. The y-intercept shape of the graph and the y-intercept
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does not change. do not change.
2
f(x) f(x) = x – 5x + 6 f(x)
2
15 f(x) = –x + 2x + 15 Form 4
f(x) = –x – 2x + 15
2
6 0 x
x
0
f(x) = 1 2 x – 5x + 6
2
(b) When c changes from 15 to 5, the graph
(b) When a changes from 1 to 2, the width moves 10 units vertically downwards.
of the graph decreases. The y-intercept The y-intercept is 5. The shape of the
does not change. graph does not change.
2
f(x) = 2x – 5x + 6 f(x)
f(x)
15 f(x) = –x + 2x + 15
2
f(x) = x – 5x + 6 5
2
6 0 x
x
0
f(x) = –x + 2x + 5
2

Example 10
The diagram below shows the graph of
Quiz
2
f(x) = –x + 2x + 15 where a = –1, b = 2 Quiz .
Quiz
Quiz
and c =15.
Penerbitan 15 0 f(x) = –x + 2x + 15 Example 11
In Example 10, if b = 0, the vertex is
at
2
x
Determine the type of roots for the
Make generalisations on the shape and
position of the graph when
f(x) = 0. Then, sketch the graph and make
(a) the value of b changes to –2.
a generalisation about the position of the
(b) the value of c changes to 5. following quadratic functions when
graph on the x-axis.
2
Hence, sketch the new graph of f(x). (a) f(x) = 3 – 6x + 2x
(b) f(x) = –9x + 12x – 4
2
23

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