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Jawaban:
Bentuk umum fungsi kuadrat
f(x) = ax² + bx + c dengan a ≠ 0
melalui (-1, 1), (0, -4), (1, -5)
• (0, -4)
=> f(0) = -4
=> a(0)² + b(0) + c = -4
=> 0 + 0 + c = -4
=> c = -4 ....... (1)
• (-1, 1)
=> f(-1) = 1
=> a(-1)² + b(-1) + c = 1
=> a - b + (-4) = 1
=> a - b = 5 ....... (2)
• (1, -5)
=> f(1) = -5
=> a(1)² + b(1) + c = -5
=> a + b + (-4) = -5
=> a + b = -1 ....... (3)
Eliminasi (2) dan (3)
a - b = 5
a + b = -1
-------------- +
2a = 4
a = 2
a + b = -1
2 + b = -1
b = -3
Jadi persamaan fungsi kuadrat tersebut adalah
f(x) = ax² + bx + c
f(x) = 2x² + (-3)x + (-4)
f(x) = 2x² - 3x – 4
