Question

Diketahui fungsi y = -5x2 + 5x + 30 dimana x anggota bilangan real (riil).
Daerah hasil fungsi tersebut adalah…

Answer 1

Persamaan Kuadrat

y = -5x² + 5x + 30

titik puncak

x = -b/2a = -5/2(-5) = 1/2

y = -5(1/2)² + 5(1/2) + 30

y = 31 1/4 = 31,25

Daerah hasil

= {y | y ≤ 31,25, y ∈ R}

Answer 2

y = -5x² + 5x + 30

a = -5

b = 5

c = 30

D = b² - 4ac

D = 5² - 4(-5)(30)

D = 25 + 600

D = 625

Sumbu simetri => x = -b/2a

= -5/2(-5)

= -5/-10

= 1/2

Nilai maksimum => masukkan x = 1/2 kerumus fungsi, maka :

f(1/2) = -5(1/2)² + 5(1/2) + 30

f(1/2) = -5 × 1/4 + 5/2 + 30

f(1/2) = -5/4 + 5/2 + 30

f(1/2) = -5/4 + 10/4 + 30

f(1/2) = 5/4 + 30

f(1/2) = 1 1/4 + 30

f(1/2) = 31 1/4

Jadi, himpunan daerah hasil :

= {y | - ∞ ≤ y ≤ 31 1/4, y € R}

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Mapel : Matematika

Materi : Fungsi