Jawaban:
C.  f(x) = x² - x - 6
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Penjelasan dgn langkah²
Diketahui:
Pers. kuadrat
f(x) = ax² + bx + c
Lewat (0, -6)
maka c = -6
f(x) = ax² + bx - 6
Lewat (3, 0) dan (-2, 0)
maka f(3) = 0, f(-2) = 0
f(3) = ax² + bx - 6
0 = (3)²a + 3b - 6
0 = 9a + 3b - 6
9a + 3b = 6
dan
f(-2) = ax² + bx - 6
0 = (-2)²a + (-2b) - 6
0 = 4a - 2b - 6
4a - 2b = 6
Eliminasi
9a + 3b = 6 (-2) = -18a - 6b = -12
4a - 2b = 6 (3) = 12a - 6b = 18
maka
-18a-12a = -12-18
-30a = -30
a = 1
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4a - 2b = 6
4(1) - 2b = 6
4 - 2b = 6
2b = 4 - 6
2b = -2
b = -1
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Pers. kuadrat
f(x) = ax² + bx + c
f(x) = 1x² - 1x - 6
f(x) = x² - x - 6
Opsi C.