Page 13 - TOP ONE ADDMATHS TG4

Additional Mathematics Form 4 Chapter 2 Quadratic Functions

16. Solve the following problems. PL 4
Selesaikan masalah-masalah berikut.

Example (a) The diagram shows the graph of quadratic
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Given the quadratic function f(x) = x + 6x – 5 has function f(x) = (x – p) – 8.
a minimum point (h, k), find Rajah di bawah menunjukkan graf bagi fungsi kuadratik
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Diberi fungsi kuadratik f(x) = x + 6x – 5 mempunyai titik f(x) = (x – p) – 8.
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minimum (h, k), cari f(x)
(i) the values of h and k,
nilai-nilai h dan k,
(ii) the equation of the axis of symmetry,
persamaan paksi simetri, –3 0 1 x
(iii) the minimum value of f(x).
nilai minimum f(x).
Find / Cari
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(i) f(x) = x + 6x – 5 (i) the equation of the axis of symmetry,
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persamaan paksi simetri,
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= x + 6x +   2 – 5 –   2 (ii) the value of p,
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= x + 6x + (3) – 5 – (3) 2 nilai p,
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= (x + 3) – 5 – 9 (iii) the coordinates of the minimum point.
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= (x + 3) – 14 koordinat bagi titik minimum.
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∴ h = –3 and k = –14
(i) x = –3 + 1 (ii) p = –1
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(ii) x = –3 2
= – (iii) (–1, –8)
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(iii) –14 = –1
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(b) A quadratic function is given by f(x) = –x + 8x (c) The quadratic function f(x) = ax + bx + c has the
+ k , where k is a constant. Find minimum point (–2, –9) and f(–1) = –7. Find
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Suatu fungsi kuadratik diberi oleh f(x) = –x + 8x + k , Fungsi kuadratik f(x) = ax + bx + c mempunyai titik
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dengan keadaan k ialah pemalar. Cari minimum (–2, –9) dan f(–1)= –7. Cari
(i) the equation of the axis of symmetry, (i) the values of a, b and c,
persamaan paksi simetri, nilai-nilai a, b dan c,
(ii) the possible values of k if the quadratic (ii) the equation of the axis of symmetry.
function f(x) has a maximum value of 25. persamaan paksi simetri.
nilai-nilai k yang mungkin jika fungsi kuadratik f(x)
mempunyai nilai maksimum 25. (i) In the form f(x) = a(x – h) + k
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h = –2, k = –9
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(i) f(x) = –x + 8x + k 2 ∴ f(x) = a(x + 2) – 9
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= –[x – 8x – k ] = a(x + 4x + 4) – 9
= ax + 4ax + 4a – 9
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
2
8



2
= – x – 8x + – 8  2 – k – – 2  Comparing: 2
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= –[x – 8x + (–4) – k – (–4) ] ax + bx + c = ax + 4ax + 4a – 9
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∴ b = 4a and c = 4a – 9
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= –[(x – 4) – k – 16]
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= –(x – 4) + k + 16 f(–1) = a(–1) + 4a(–1) + 4a – 9
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–7 = a – 4a + 4a – 9
Therefore, the equation of axis of symmetry –7 = a – 9
is x = 4. a = 2
(ii) k + 16 = 25 b = 4(2)
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k = 9 = 8
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k = ±√9
k = 3 or k = –3 c = 4(2) – 9
= –1
(ii) x = –2
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