Bonjour,
Comme f(0)=1, on a :
[tex]a\times 0^{2}+b\times 0 + c = 1\\c=1[/tex]
f(x) = ax² + bx + 1
[tex]\left\{\begin{array}{l} a(-1)^{2}-b + 1 = -1 \\a(-2)^{2}-2b+1=1\end{array}\right \\\left\{\begin{array}{l} a-b= -2\\4a-2b=0\end{array}\right \\\left\{\begin{array}{l} a-b=-2\\2a-b=0\end{array}\right \\\left\{\begin{array}{l} 2a-b-a+b=2\\ b=a+2\end{array}\right \\\left\{\begin{array}{l}a=2 \\b=4\end{array}\right[/tex]
f(x) = 2x²+4x+1
