Question

Care este functia de gradul al 2 lea al carei grafic contine punctele A(3,2) B(-1,6) C(-2,12)

Answer 1

f(x)=ax²+bx+c
f(3)=2
f(-1)=6
f(-2)=12

(1)9a+3b+c=2
(2)a-b+c=6
(3)4a-2b+c=12

(1)+(2)+(3)
9a+3b+c+a-b+c+4a-2b+c=20
14a+3c=20
(2)*(-2)+(3)
-2a+2b-2c+4a-2b+c=24

2a-c=24/*(3)
14a+3c=20

(4)6a-3c=72
(5)14a+3c=20
(4)+(5)
20a=82
a=82/20=41/10
-c=24-82/20
c=-398/20=-199/10

a-b+c=6
41/10-b-199/10=6
41-10b-199=60
-10b=60+199-41
-10b=218
b=-218/10


f(x)= 41x²/10-218x/10-199/10