Jawaban:

c. y = x² - 5x + 4

Penjelasan dengan langkah-langkah:

persamaan parabola

y = ax² + bx + c

melalui titik (2, -2), (4, 0) dan (-1, 10)

melalui titik (2, -2)

-2 = a(2)² + b(2) + c

4a + 2b + c = -2 ................(1)

melalui titik (4, 0)

0 = a(4)² + b(4) + c

16a + 4b + c = 0 ...............(2)

melalui titik (-1, 10)

10 = a(-1)² + b(-1) + c

a - b + c = 10 ..................(3)

eliminasi (1) dan (2)

4a + 2b + c = -2

16a + 4b + c = 0

-------------------------- --

-12a - 2b = - 2

6a + b = 1 .......................(4)

eliminasi (1) dan (3)

4a + 2b + c = -2

a - b + c = 10

-------------------------- -

3a + 3b = -12

a + b = -4 ........................(5)

eliminasi (4) dan (5)

6a + b = 1

a + b = -4

------------------- -

5a = 5

a = 1..subtitusikan a = 1 ke (5)

a + b = -4

1 + b = -4

b = -4 - 1

b = -5...subtitusikan a = 1 dan b = 3 ke 3

a - b + c = 10

1 - (-5)+ c = 10

c = 10 - 5 - 1

c = 4

y = ax² + bx + c

y = x² - 5x + 4