Application Of Integration

If $$\left[\begin{array}{lll}4 a^{2} & 4 a & 1 \\ 4 b^{2} & 4 b & 1 \\ 4 c^{2} & 4 c & 1\end{array}\right]\left[\begin{array}{c}f(-1) \\ f(1) \\ f(2)\end{array}\right]=\left[\begin{array}{c}3 a^{2}+3 a \\ 3 b^{2}+3 b \\ 3 c^{2}+3 c\end{array}\right], \quad f(x)$$

is a quadratic function and its maximum value occurs at a point \(\mathrm{V}\). If A is a point of intersection of \(y=f(x)\) with \(x\)-axis and point B is such that chord AB subtends a right angle at point \(\mathrm{V}\). Find the area enclosed by \(f(x)\) and chord AB.