Question

Seja a funçao f(x) = 3x²-bx + c , em que f(2) = 10 e f(-1) =3 . Calcule b , c e o valor da expressao f(3) + 2.f(1)

Answer 1

f(x) = 3x² - bx + c

f(2) = 10
3.2² - 2b + c = 10
3.4 - 2b + c = 10
12 - 2b + c = 10
- 2b + c = 10 - 12
- 2b + c = - 2 ①

f(-1) = 3
3.(-1)² - (-1)b + c = 3
3.1 + b + c = 3
b + c = 3 - 3
b + c = 0 ②

{- 2b + c = - 2
{b + c = 0 *(-1)
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾
- 2b + c = - 2
- b - c = 0
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- 3b = - 2
b = 2/3

b + c = 0
c = - b
c = - 2/3

f(x) = 3x² - 2x/3 - 2/3

f(3) = 3.3² - 2.3/3 - 2/3
f(3) = 3.9 - 2 - 2/3
f(3) = 27 - 2 - 2/3
f(3) = 25 - 2/3
f(3) = (75 -2)/3
f(3) = 73/3

f(1) = 3.1² - 2.1/3 - 2/3
f(1) = 3.1 - 2/3 - 2/3
f(1) = 3 - 4/3
f(1) = (9 - 4)/3
f(1) = 5/3

f(3) + 2f(1)
= 73/3 + 2.5/3
= 73/3 + 10/3
= 83/3

R.: 83/3