Răspuns:
f(x) = x² -3x +2
Explicație pas cu pas:
A(1,0) , B(2,0), C(3,2) ∈ Gf
f(x) = ax² + bx + c
A(1 , 0) ∈ Gf <=> f(1) = 0 => a·1²+b·1+c = 0 => a+b+c = 0
B(2 , 0) ∈ Gf <=> f(2) = 0 => a·2²+b·2+c = 0 => 4a+2b+c = 0
C(3 , 2) ∈ Gf <=> f(3) = 2 => a·3²+b·3+c = 2 => 9a+3b+c = 2
a + b = - c
4a + 2b = -c => a+b = 4a+2b <=> 3a = -b => b = -3a
9a -9a + c = 2 => c = 2
a+b = -2 ; b = -3a => a -3a = -2 <=> -2a = -2 => a = 1
b = -3 =>
f(x) = x² -3x +2
