Page 8 - PRAKTIS HEBAT ADDMATHS TG4

Additional Mathematics Form 4 Practice 2 Quadratic Functions
38. f(x) 45. Determine the maximum value and the
(m, n) corresponding value at x for the quadratic
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function f(x) = –x + 4x – 8. PL 3
Tentukan nilai maksimum dan nilai x yang
sepadan bagi fungsi kuadratik f(x) = –x + 4x – 8.
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x
0 p 6
46. Given the quadratic function f(x) = x – 5x + 4
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has the minimum point at (p, q). Find PL 3
The diagram above shows the graph of a Diberi fungsi kuadratik f(x) = x – 5x + 4
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quadratic function for f(x) = 4 – (x – 4) . Find mempunyai titik minimum pada (p, q). Cari
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the values of PL 3 (a) the value of p and of q.
Rajah di atas menunjukkan graf bagi fungsi nilai p and nilai q.
kuadratik f(x) = 4 – (x – 4) . Cari nilai bagi
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(a) m (b) n (b) the equation of the axis of symmetry.
(c) p persamaan paksi simetri.
47. Given f(x) = x – kx + 2k – 3, such that k is a
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39. Given the quadratic function f(x) = –x + 6x – 13. constant, is always positive when m , k , n.
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Without drawing the graph, find the maximum Find the value of m and of n. PL 4
point of f(x). PL 3 Diberi f(x) = x – kx + 2k – 3, dengan keadaan
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Diberi fungsi kuadratik f(x) = –x + 6x – 13. k ialah pemalar, adalah sentiasa positif
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Tanpa melukis graf, cari titik maksimum bagi apabila m , k , n. Cari nilai m dan nilai n.
f(x).
48. The quadratic function f(x) = (x + 4) – 20 + k,
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40. Determine the type of roots for the following where k is a constant, has minimum point
quadratic function f(x) = 0. PL 3 (–4, 5k). PL 3
Tentukan jenis punca bagi fungsi kuadratik Fungsi kuadratik f(x) = (x + 4) – 20 + k,
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f(x) = 0 yang berikut. dengan keadaan k ialah pemalar, mempunyai
(a) f(x) = x – 4x – 18 titik minimum (–4, 5k).
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(b) f(x) = –5x + 11x – 7 (a) Find the value of k.
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Cari nilai k.
41. Find the range of values of x such that the (b) State the type of roots for f(x) = 0. Justify
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SPM quadratic function f(x) = 3x – 14x – 5 is
2017 your answer.
negative. PL 4 Nyatakan jenis punca bagi f(x) = 0.
Cari julat nilai x dengan keadaan fungsi Justifikasikan jawapan anda.
kuadratik f(x) = 3x – 14x – 5 ialah negatif.
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49. Given that the graph of a quadratic function
42. Find the range of values of m if the quadratic f(x) = mx – 6x + n, where m and n are
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function f(x) = x – 4x + m intersects the x-axis constants, has a minimum point. PL 4
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at two different points. PL 4 Diberi bahawa graf bagi fungsi kuadratik
Cari julat nilai m jika graf bagi fungsi f(x) = mx – 6x + n, dengan keadaan m dan n
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kuadratik f(x) = x – 4x + m menyilang paksi-x ialah pemalar, mempunyai titik minimum.
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pada dua titik yang berlainan. (a) Given m is an integer such that –2 , m , 2,
state the value of m.
43. Find the value of p if f(x) = px + 5x – 6 Diberi m ialah integer dengan keadaan
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touches the x-axis at one point only. PL 4 –2 , m , 2, nyatakan nilai m.
Cari nilai p jika f(x) = px + 5x – 6 menyentuh
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paksi-x pada satu titik sahaja. (b) Using the answer from (a), find the value
of n when the graph touches the x-axis at
44. Find the minimum value and the equation of the one point only.
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axis of symmetry for f(x) = x – 3x + 4. PL 3 Dengan menggunakan jawapan daripada
Cari nilai minimum dan persamaan paksi (a), cari nilai n apabila graf tersebut
simetri untuk f(x) = x – 3x + 4. menyentuh paksi-x pada satu titik sahaja.
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