Question

Jika fungsi kuadrat f(x)= ax^2 +bx + c mempunyai titik puncak (2,1) dan melalui titik (-1,10) maka nilai a + b + c =.....

Answer 1

Titik puncak x = -b/2a

-b/2a = 2
-b = 4a
b = -4a

f (x) = ax² + bx + c
f (x) = ax² - 4ax + c

f (2) = 1
1 = a(2)² - 4a(2) + c
1 = 4a - 8a + c
1 = -4a + c
c = 4a + 1

f (x) = ax² - 4ax + c
f (x) = ax² - 4ax + 4a + 1

f (-1) = 10
10 = a(-1)² - 4a(-1) + 4a + 1
10 = a + 4a + 4a + 1
10 = 9a + 1
9a = 10 - 1
9a = 9
a = 9/9
a = 1

f (x) = (1)x² - 4(1)x + 4(1) + 1
f (x) = x² - 4x + 5

a = 1
b = -4
c = 5

a + b + c = 1 - 4 + 5
= 2