❐ Fungsi Kuadrat

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Diketahui

• Titik balik (5,-4)
• Melalui titik (3,0)

Ditanyakan

Fungsi kuadrat = _?

Jawab

Persamaan umum fungsi kuadrat

f(x) = ax² + bx + c

Persamaan titik balik

x = -b/2a

5 = -b/2a

5 x 2a = -b

10a = -b

b = -10a

Substitusikan b = -10a

f(x) = ax² + bx + c

f(x) = ax² + (-10a)x + c

f(x) = ax² - 10ax + c

Substitusikan x = 3

f(x) = ax² - 10ax + c

f(3) = a(3)² - 10a(3) + c

0 = 9a - 30a + c

0 = -21a + c

c = 21a

Substitusikan c = 21a

f(x) = ax² - 10ax + c

f(x) = ax² - 10ax + 21a

Substitusikan x = 5

f(x) = ax² - 10ax + 21a

f(5) = a(5)² - 10a(5) + 21a

-4 = 25a - 50a + 21a

-4 = -4a

a = 1

Substitusikan a = 1

b = -10a = -10(1) = -10

c = 21a = 21(1) = 21

Persamaan fungsi kuadratnya

f(x) = ax² + bx + c

f(x) = x² - 10x + 21