Jawaban:

titik balik fungsi f(x) tersebut adalah (1, -9)

Penjelasan dengan langkah-langkah:

f(x) = ax² + bx + c

• melewati titik (4 , 9)

x = 4 , y = 9

f(4) =a × 4² + b × 4 + c

9 = 16a + 4b + c

16a + 4b + c = 9 .... (1)

• melewati (3 , -1)

x = 3 , y = -1

f(3) = a × 3² + b × 3 + c

-1 = 9a + 3b + c

9a + 3b + c = -1 ... (2)

• melewati (-5 , 63)

x = -5 , y = 63

f(-5) = a × (-5)² + b × (-5) + c

63 = 25a - 5b + c

25a - 5b + c = 63 ... (3)

SPLTV

16a + 4b + c = 9 ... (1)

9a + 3b + c = -1 ... (2)

25a - 5b + c = 63 ... (3)

• (1) - (3)

16a + 4b + c = 9

25a - 5b + c = 63

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

-9a + 9b = - 54

-9(a - b) = -54

a - b = -54 ÷ (-9)

a - b = 6

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

• (1) - (2)

16a + 4b + c = 9

9a + 3b + c = -1

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

7a + b = 10 ... (5)

substitusi (4) ke (5)

7(b + 6) + b = 10

7b + 42 + b = 10

8b = 10 - 42

8b = -32

b = -32 ÷ 8

b = -4

substitusi b = -4 ke (4)

a = -4 + 6

a = 2

substitusi a = 2 , b = -4 ke (2)

9 × 2 + 3 × (-4) + c = -1

18 - 12 + c = -1

6 + c = -1

c = -1 - 6

c = -7

substitusi a = 2 , b = -4 , c = -7 ke bentuk fungsi f(x) = ax² + bx + c

f(x) = 2x² - 4x - 7

Titik balik fungsi f(x) = (Xp , Yp)

• Xp = - b/2a

Xp = - (-4)/2(2)

Xp = 4/4

Xp = 1

• Yp = f(Xp)

Yp = f(1)

Yp = 2 × 1² - 4 × 1 - 7

Yp = 2 - 4 - 7

Yp = -9

(Xp , Yp) = (1 , -9)