Page 41 - Hybrid PBD 2022 Form 4 Additional Mathematics

Matematik Tambahan Tingkatan 4 Bab 2 Fungsi Kuadratik
13. Ungkapkan setiap fungsi kuadratik yang berikut dalam bentuk am dan bentuk pintasan. SP 2.3.3 TP3
Express each of the following quadratic functions in the general form and intercept form. Nota
Visual
2
Tip Penting (a) f(x) = –(x + 1) + 4
f(x) = 16 – (x + 3) 2
Bentuk pintasan / Intercept form f(x) = –(x + 2x + 1) + 4
2
f(x) = 16 – (x + 6x + 9) f(x) = a(x – p)(x – q) = –x – 2x + 3 → Bentuk am / General form
2
2
= –x – 6x + 7 → Bentuk am / General form = –(x + 2x – 3)
2
2
= –(x + 6x – 7) = –(x – 1)(x + 3) → Bentuk pintasan
2
= –(x – 1)(x + 7) → Bentuk pintasan / Intercept form Intercept form


(b) f(x) = 2 x – 3  2 – 49 (c) f(x) = 3 x – 1  2 – 27
4 8 2 4
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
3

2
2
f(x) = 2 x – x + 9  – 49 f(x) = 3 x – x + 1  – 27
2 16 8 4 4
9
= 2x – 3x + – 49 = 3x – 3x + 3 – 27
2
2
8 8 4 4
2
2
= 2x – 3x – 5 → Bentuk am / General form = 3x – 3x – 6 → Bentuk am / General form
= (2x – 5)(x + 1) = 3(x + 1)(x – 2) → Bentuk pintasan

= 2 x – 5  (x + 1) → Bentuk pintasan Intercept form
2 Intercept form
14. Ungkapkan setiap fungsi kuadratik yang berikut dalam bentuk verteks. Kemudian, nyatakan koordinat vertex
dan paksi simetri graf fungsi itu. SP 2.3.3 TP3
Express each of the following quadratic functions in the vertex form. Hence, state the coordinates of vertex and axis of symmetry of the
graph of the function.
(a) f(x) = (x + 8)(x + 2)
f(x) = (x + 5)(x – 7) Tambah dan tolak
Adding and subtracting f(x) = x + 2x + 8x + 16
2
f(x) = x – 7x + 5x – 35   2 2
2
–2
2
= x – 2x – 35 2 = (–1) = x + 10x + 16
2
2
2
2
2
= x – 2x + (–1) – (–1) – 35 = x + 10x + 5 – 5 + 16
2
2
2
= (x – 1) – 36 = (x + 5) – 9
2
Verteks / Vertex: (1, –36) Verteks / Vertex : (–5, –9)
Paksi simetri / Axis of symmetry: x = 1 Paksi simetri / Axis of symmetry: x = –5
(b) f(x) = 6 – 8x – x 2 (c) f(x) = 3x – 18x + 4
2

f(x) = –(x + 8x – 6) f(x) = 3 x – 6x + 4 
2
2
= –(x + 8x + 4 – 4 – 6) 3
2
2
2

2
2
2
2
= –(x + 4) + 22 = 3 x – 6x + (–3) – (–3) + 4 
3
Verteks / Vertex : (–4, 22) = 3(x – 3) – 23
2
Paksi simetri / Axis of symmetry: x = –4
Verteks / Vertex : (3, –23)
Paksi simetri / Axis of symmetry: x = 3
(d) f(x) = (x + 2) – 8x – 2 (e) f(x) = 3 – 5x – 2x 2
2
5

f(x) = x + 4x + 4 – 8x – 2 f(x) = –2 x + x – 3 
2
2
= x – 4x + 2 2 2
2
3
5
2
2

5
5
= x – 4x + (–2) – (–2) + 2 = –2 x + x +     
2
2
2
–
–
2
= (x – 2) – 2 2 2 4 4 2
2

Verteks / Vertex : (2, –2) = –2 x + 5  + 49
8
4
Paksi simetri / Axis of symmetry: x = 2 5 49

Verteks / Vertex : – , 
4 8
Paksi simetri / Axis of symmetry: x = – 5
4
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