Jawaban:

NOMOR 1 :

• bentuk umum fungsi kuadrat f(x) = ax² + bx + c dengan a ≠ o

Melalui (-1,1) , (0,-4) , (1,-5)

• (0,-4)

=> f(0) = -4

a(0)² + b(0) + c = -4

0+0+C = -4

C = -4 (1)

• (1,-5)

=> f(1) = -5

a(1)² + b(1) + c = -5

a + b + (-4) = -5

a + b = -1 (3)

Eliminasi (1) dan (2) :

a-b = 5

a+b = -1

------------+

2a = 4

a = 2

a+b = 1

2+b = -1

b = -3

Jadi, persamaan fungsi kuadrat tersebut adalah

f(x) = ax² + bx + c

f(x) = 2x² + (-3)x + (-4)

f(x) = 2x² - 3x - 4

NOMOR 2

(4,0) => f(4) = 0

(-3,0) => f(-3) = 0

bentuk bentuk umum fungsi kuadrat :

f(x) = ax² + bx + c

maka,

f(4) = 0

=> 16a + 4b + c = 0 (1)

=> C = -16a - 4b

f(-3) = 0

=> 9a - 3b + c = 0 (2)

=> C = - 9a + 3b

f(2) = -10

4a + 2b + c = -10 (3)

maka :

9a - 3b + c = 0

=> 9a - 3b - 16a - 4b = 0

=> -7a - 7b = 0

=> -a - b = 0

=> -a = b

dan

4a + 2b + c = -10

=> 4a + 2b - 9a + 3b = -10

=> -5a + 5b = -10

=> -a + b = -2

=> b + b = -2

=> 2b = -2

=> b = -1

Sehingga

a = -b

a = -(-1)

a = 1

dan

c = -9a + 3b

c = -9(1) + 3(-1)

c = -9 - 3

c = -12

didapat a = 1 , b = -1 , c = -12.

Jadi, rumus fungsi kuadratnya ialah

f(x) = ax² + bx + c

=> f(x) = (1)x² + (-1)x + 12

=> f(x) = x² - x - 12

JADIKAN JAWABAN TERBAIK YAAA