[tex]f(x) = ax^2+bx+c \\ \\ f'(x) = 2ax+b[/tex]
Gf e tangent cu axa Ox in punctul (1,0)
[tex]\Rightarrow f'(1) = 0 \Rightarrow 2a+b = 0\\ \\\Rightarrow f(1) = 0 \Rightarrow a+b+c = 0[/tex]
Gf trece prin (0,2)
[tex]\Rightarrow f(0) = 2 \Rightarrow c = 2 \\ \\ \begin{cases} 2a+b = 0 \\ a+b = -2\end{cases}\Bigg| \Rightarrow a = 2,\quad b = -4,\quad c = 2\\ \\\\ \Rightarrow \boxed{f(x) = 2x^2-4x+2}[/tex]
