Question

Seja a função quadrática f(x) = ax² + bx + c, em que f(1) = 3 e f(-2) =
24. Nessas condições, determine:
a) Os valores de a e b
b) F(3)

Answer 1

Oi.

f(x) = ax² +bx +c

f(1) = a(1)² +b(1) +c = a +b +c

f(-2) = a(-2)² +b(-2) +c = 4a -2b +c

f(1) = 3

f(-2) = 24

$\left \{ {{a +b +c = 3} \atop {4a -2b +c = 24}} \right.$

a = 3 -b -c

4a -2b +c = 24

4(3 -b -c) -2b +c = 24

12 -4b -4c -2b +c = 24

-6b -3c = 12

-6b = 12 +3c

$-b=\frac{12+3c}{6}$

$-b=2+\frac{c}{2}$

$b=-2-\frac{c}{2}$

a = 3 -b -c

$a=3-(-2-\frac{c}{2})-c$

$a=3+2+\frac{c}{2}-c$

$a=5+\frac{c-2c}{2}$

$a=5-\frac{c}{2}$

a)

$a=5-\frac{c}{2}$

$b=-2-\frac{c}{2}$

b)

f(x) = ax² +bx +c

f(3) = a(3)² +b(3) +c =

= 9a +3b +c

$= 9(5-\frac{c}{2}) +3(-2-\frac{c}{2}) +c$

$= 45-\frac{9c}{2} -6-\frac{3c}{2} +c$

$= 39-\frac{9}{2}c -\frac{3}{2}c +c$

$= 39-\frac{12}{2}c +c$

$= 39-6c +c$

$=39-5c$