Substitusi a = 3/2:
6 . 3/2 + 2b = 12
9 + 2b = 12
2b = 3
b = 3/2
a + b + c = 1
3/2 + 3/2 + c = 1
c = -2
Mencari U100:
Un = an^2 + bn + c
U100 = 3/2(100)^2 + 3/2(100) + (-2)
U100 = 3/2. 10000 + 3/2. 100 – 2
U100 = 15000 + 150 – 2
U100 = 15148
5. Diketahui suatu barisan 0, -9, -12, … suku ke-n dari barisan tersebut dapat dihitung dengan rumus Un = an2 + bn + c. Tentukan nilai minimum dari barisan tersebut.
Jawab:
0, -9, -12, …
Un = an^2 + bn + c
U1 = 0
a(1)^2 + b(1) + c = 0
a + b + c = 0
c = - a – b
U2 = -9
a(2)^2 + b(2) + c = -9
4a + 2b + c = -9
4a + 2b + (-a-b) = -9
4a + 2b – a – b = -9
3a + b = -9
U3 = -12
a(3)^2 + b(3) + c = -12
9a + 3b + c = -12
9a + 3b + (-a – b) = -12
8a + 2b = -12
4a + b = -6
Baca Juga: Kunci Jawaban Matematika Kelas 9 Halaman 83, Kegiatan 1 Cara Menggambar Grafik Fungsi Kuadrat
3a + b = -9
4a + b = -6
-a = -3
a = 3
3a + b = -9
3(3) + b = -9
b = -18
c = -a – b
c = - 3 + 18 = 15
Un = 3n^2 – 18n + 15
Nilai minimum turunan:
6n – 18 = 0
6n = 18
n = 3
Nilai minimum saat n = 3
U3 = -12
6. Fungi kuadrat y = f(x) melalui titik (3,-12) dan (7, 36). Jika sumbu simetrinya x = 3, tentukan nilai minimum fungsi f(x).
Jawab:
Sumbu simetri
x = 3
-b/2a = 3
(3,-12) dan (7, 36)
y = ax^2 + bx + c
-12 = a(3)^2 + b(3) + c
-12 = 9a + 3b + c
c = -9a – 3b – 12
36 = a(7)^2 + b(7) + c
36 = 49a + 7b + c
c = 36 – 49a – 7b
-9a – 3b – 12 = 36 – 49a – 7b
49a -9a + 7b - 3b = 12 + 36
40a + 4b = 48
10a + b = 12 …..(1)