Page 73 - Matematik Tambahan Tingkatan 4 KSSM

Fungsi Kuadratik

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RUMUSAN BAB
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(x – )(x – ) = 0

Penyempurnaan
atau
kuasa dua k��d�� x – ( + )x + = 0 Lakaran graf
m��b��t�� k��d�� BAB 2
2

p��s��a��
Rumus ��n��l��a��n Garis nombor
p��y��e��i��
Persamaan kuadratik Ketaksamaan Jadual
ax + bx + c = 0 kuadratik
2
a > 0, graf bentuk
m��i��t��n FUNGSI KUADRATIK a < 0, graf berbentuk
Jenis–jenis
punca Untuk a > 0,
Pembezalayan b > 0, verteks di kiri paksi-y
D = b – 4ac k��a��p��u��h��
2
Fungsi kuadratik b < 0, verteks di kanan paksi-y
c bertambah, graf bergerak ke atas
Bentuk am c berkurang, graf bergerak ke bawah
f(x) = ax + bx + c
2
Dua punca nyata
dan berbeza, k��a��p��u��h��
D > 0 a > 0, graf bentuk
Bentuk verteks a < 0, graf berbentuk
2
f(x) = a(x – h) + k
Dua punca
sama, D = 0 h bertambah, graf bergerak ke kanan
Bentuk pintasan h berkurang, graf bergerak ke kiri
f(x) = a(x – p)(x – q)
Tiada punca
k bertambah, graf bergerak ke atas
nyata, D < 0
k berkurang, graf bergerak ke bawah
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N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
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A
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A
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A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
N
D
N
N
N
D
D
D
D
D
N
N
N
N
N
N
N
N
N
N
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
S
S
S
S
S
S
S
S
S
S
S
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S
S
S
S
S
S
S
S
S
S
S
S
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S
S
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S
S
S
S
S
S
S
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S
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S
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S
S
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S
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S
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S
S
S
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S
S
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S

I
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U
U
U
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L
L
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L
L
L
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L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
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L
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U
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TULIS JURNAL ANDA
T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T
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U
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U
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U
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U
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L
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I
I
I
I
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I
I
I
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I
I
I
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I
I
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I
I
I
I
I
I
I
I
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I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
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L
L
L
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I
I
L
L
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L
L
L
L
L
L
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L
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I
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I
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I
I
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I
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I
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I
I
I
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I
I
I
I
I
I
I
I
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I
I
I
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I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
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R
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R
R
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R
R
R
R
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R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
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R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
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N
N
N
N
N
N
N
N
N
N
N
N
N
N
R
N
N
R
R
R
N
N
N
N
N
N
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R
R
R
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R
R
R
R
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R
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R
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R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
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N
A
A
A
A
A
A
A
A
A
A
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A
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A
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A
A
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A
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A
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A
A
A
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A
A
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A
A
A
A
A
A
A
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A
A
A
A
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A
A
A
A
A
A
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A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
A
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A
A
A
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A
A
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A
A
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A
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A
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A
A
A
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A
A
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A
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A
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A
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A
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A
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A
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N
N
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N
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Perkataan kuadratik berasal daripada perkataan quad yang bermaksud empat tetapi suatu
persamaan kuadratik melibatkan polinomial dengan kuasa tertinggi 2. Buat kajian tentang
asal usul perkataan kuadratik yang berkaitan dengan persamaan kuadratik. Hasilkan satu folio

grafik tentang kajian anda.
65