Jawab:

Penjelasan dengan langkah-langkah:

11. 2x² + 2x - 4 = 0

2(x² + x - 2) = 0

2(x + 2) (x - 1) = 0

x + 2 = 0

x = -2

x - 1 = 0

x = 1

13. 2x² + 7x - 15 = 0

(2x - 3) (x + 5) = 0

2x - 3 = 0

2x = 3

x = 3/2

x + 5 = 0

x = -5

15. x² - 2x - 3 = 0

(x + 1) (x - 3) = 0

x + 1 = 0

x = -1

x - 3 = 0

x = 3

x1 > x2

x1 = 3 dan x2 = -1

x1 - x2 = 3 - (-1) = 4

17. Titik potong kurva terhadap sumbu X diperoleh jika y = 0.

2x² + 3x - 2 = 0

(2x - 1) (x + 2) = 0

x + 2 = 0

x = -2

2x - 1 = 0

2x = 1

x = 1/2

Titik potong kurva terhadap sumbu X adalah (-2, 0) dan (1/2, 0).

Titik potong kurva terhadap sumbu Y diperoleh jika x = 0.

y = 2(0)² + 3(0) - 2

y = -2

Titik potong kurva terhadap sumbu Y adalah (0, -2).

19. y = 8 - 2x - x²

a = -1 ; b = -2 ; c = 8

D = b² - 4ac

D = (-2)² - 4 (-1) (8)

D = 4 + 32

D = 36

Titik balik = (-b/2a, -D/4a)

Titik balik = (-(-2)/2(-1), -36/4(-1))

Titik balik = (2/(-2), 36/4)

Titik balik = (-1, 9)

21. y = x² + 2x - 5

a = 1 ; b = 2

Persamaan sumbu simetri : x = -b/2a

x = -2/2(1)

x = -2/2

x = -1

23. y = 2x² + 3x - 2m

a = 2 ; b = 3 ; c = -2m

D = 3² - 4 (2) (-2m)

D = 9 + 16m

Nilai minimum = -D/4a

-1 5/8 = -D/4a

13/8 = (9 + 16m)/4(2)

9 + 16m = 13

16m = 13-9

16m = 4

m = 4/16 = 1/4

25. y = -2x² + 5x - 7

a = -2 sehingga a < 0 dan grafik membuka ke bawah

D = 5² - 4 (-2) (-7)

D = 25 - 56

D = -31

D < 0 sehingga grafik di bawah sumbu X