Page 19 - Ranger SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 2 Quadratic Functions

Example 18
Quiz The diagram below shows the graph of
Quiz
Quiz
Quiz
2
In Example 16, if the value of h the quadratic function f(x) = a(x – m) + n,
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changes from 2 to –2, the graph will where a, m and n are constants. The straight
be reflected in . line y = –48 is the tangent to the curve at
point K.
Form 4 Example 17 2 f(x)
Sketch the graph of f(x) = x – 3x + 2.
–6 0 2 x
Solution
a  0, the shape of the graph is . K
b – 4ac = (–3) – 4(1)(2) = 1  0
2
2
The graph of f(x) intersects the x-axis at (a) State the coordinates of the point K.
two different points. (b) Find the value of a.
f(x) = x – 3x + 2 (c) State the equation of the curve if the
2
graph is reflected in the y-axis.
   
= x – 3x + – 3 2 – – 3 2 + 2 Solution
2
2
2
9

= x – 3  2 – + 2 (a) Equation of axis of symmetry,
2
4
–6 + 2

= x – 3  2 – 1 x = 2
4
2
= –2
The minimum point is  3 , – 1  . Then, K(–2, –48)
4
2
2
When f(x) = 0, (b) f(x) = a(x + 2) – 48
x – 3x + 2 = 0 At (2, 0), 2
2
(x – 1)(x – 2) = 0 0 = a(2 + 2) – 48
48 = 16a
x = 1 or x = 2 a = 3
Thus, the graph intersects the x-axis at
x = 1 and x = 2. (c) When reflected in the y-axis, the value
of m changes from –2 to 2.
When x = 0, 2
f(0) = 0 – 3(0) + 2 = 2 Thus, f(x) = 3(x – 2) – 48
2
Thus, the y-intercept is 2.
f(x)
x = 3
2
2
x
0 1 2
3 2 , – 1 4

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