Y = f(x) adalah fungsi kuadrat, f(1) = f(3) = 0 dan f(0) = -6. f(2) = .. ..
whongaliem
Misal : f(x) = ax² + bx + c f(1) = a .1² + b . 1 + c 0 = a + b + c ...... pers i f(3) = a .3² + b .3 + c 0 = 9a² + 3b + c .....pers ii f(0) = a .0² + b .0 + c - 6 = 0 + 0 + c c = - 6 elemenasi pers i dan ii a + b + c = 0 kalikan dgn 3 ------> 3a + 3b + 3c = 0 9a + 3b + c = 0 9a + 3b + c = 0 --------------------------- - - 6a + 2c = 0 - 6a = - 2c a = . c a = 1/3 . - 6 a = - 2 a + b + c = 0 - 2 + b + - 6 = 0 b - 8 = 0 b = 8 jadi , f(x) = - 2x² + 8x - 6 f(2) = - 2 .2² + 8 . 2 - 6 = - 8 + 16 - 6 = 2
f(1) = a .1² + b . 1 + c
0 = a + b + c ...... pers i
f(3) = a .3² + b .3 + c
0 = 9a² + 3b + c .....pers ii
f(0) = a .0² + b .0 + c
- 6 = 0 + 0 + c
c = - 6
elemenasi pers i dan ii
a + b + c = 0 kalikan dgn 3 ------> 3a + 3b + 3c = 0
9a + 3b + c = 0 9a + 3b + c = 0
--------------------------- -
- 6a + 2c = 0
- 6a = - 2c
a =
a = 1/3 . - 6
a = - 2
a + b + c = 0
- 2 + b + - 6 = 0
b - 8 = 0
b = 8
jadi , f(x) = - 2x² + 8x - 6
f(2) = - 2 .2² + 8 . 2 - 6
= - 8 + 16 - 6
= 2
a(0) + b(0) + c = -6
berarti c = -6
f(3) = 0
a(9) + b(3) - 6 = 0
9a + 3b = 6
f(1) = 0
a(1) + b(1) - 6 = 0
a + b = 6
3a + 3b = 18
eliminasi 9a + 3b sama 3a + 3b
6a = -12
a = -2
substitusi a ke salah satu persamaan
a + b = 6
-2 + b = 6
b = 8
setelah dapat a, b, sama c
f(x) = ax^2 + bx + c
f(x) = -2x^2 + 8x - 6
berarti
f(2) = -2(4) + 8(2) - 6
f(2) = -8 + 16 - 6
f(2) = 2