Question

Se considera functia f(x)=x^2+ax+b. Determinati numerele reale a si b pentru care graficul functiei f contine punctele A(2,3) , B(-1,0)

Answer 1

$f(x)=x^2+ax+b\\ A(2,3)\in~G_f \Leftrightarrow~f(2)=3~ \Leftrightarrow~4+2a+b=3\\B(-1,0)\in~G_f \Leftrightarrow~f(-1)=0~ \Leftrightarrow~1-a+b=0.\\ \\ Ai~sistemul~\begin{cases}~4+2a+b=3\\1-a+b=0~\end{cases}~\Leftrightarrow~\begin{cases}~a=b+1\\4+2a+b=3~\end{cases}~\Leftrightarrow~\begin{cases}~a=b+1\\~6+3b=3~\end{cases}~\Leftrightarrow~\begin{cases}~b=-1\\~a=0~\end{cases}$