Buatlah grafik parabola y=ax2 +bx+c melalui (1, -1), (4,8) dan (-1, 3). Tentukan persamaan parabola tsb.
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thanks a lot
[ Persamaan Parabola ]
y = ax² + bx + c
(1, -1) , ( 4,8) , dan (-1,3)
{Subtitusi ke persamaan}
(1,-1) → - 1 = a(1)² + b(1) + c
- a + b + c = -1
(4,8) → 8 = a(4)² + b(4) + c
- 16a + 4b + c = 8
(-1,3) → 3 = a(-1)² + b(-1) + c
- a - b + c = 3
{Buat persamaan dua variabel}
16a + 4b + c = 8
a + b + c = - 1
___________-
15a + 3b = 9
5a + b = 3 (pers 1 )
16a + 4b + c = 8
a - b + c = 3
___________-
15a + 5b = 5
3a + b = 1 (pers 2)
{Selesaikan persamaan}
5a + b = 3
3a + b = 1
_________-
2a = 2
a = 1
5a + b = 3
5(1) + b = 3
b = - 2
a + b + c = -1
1 +( - 2) + c = -1
-1 + c = -1
c = 0
- Persamaan Parabola
a = 1 , b = -2 , c = 0
y = ax² + bx + c
y = (1)x² + (-2)x + 0
y = x² - 2x
Jadi, persamaan parabolanya adalah y = x² - 2x
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