Question

Buatlah grafik parabola y=ax2 +bx+c melalui (1, -1), (4,8) dan (-1, 3). Tentukan persamaan parabola tsb.

thanks a lot

Answer 1

[ 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