Đáp án:
$\begin{array}{l}
\left\{ \begin{array}{l}
- 2 = a.1 - 4.1 + c\\
3 = a.4 - 4.2 + c
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a + c = 2\\
4a + c = 11
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = 3\\
c = - 1
\end{array} \right.\\
\Rightarrow y = 3{x^2} - 4x - 1\\
b)\left\{ \begin{array}{l}
\frac{{ - b}}{{2a}} = - 2 = \frac{4}{{2a}}\\
- 2 = a.4 + 4.2 + c
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = - 1\\
4a + c = - 10
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = 1\\
c = - 6
\end{array} \right.\\
\Rightarrow y = - {x^2} - 4x - 6\\
c)\left\{ \begin{array}{l}
\frac{{ - b}}{{2a}} = - 3\\
1 = a.4 + 4.2 + c
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
\frac{4}{{2a}} = - 3\\
a + c = - 7
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = \frac{{ - 2}}{3}\\
c = \frac{{ - 19}}{3}
\end{array} \right.\\
\Rightarrow y = \frac{{ - 2}}{3}{x^2} - 4x - \frac{{19}}{3}\\
4)\left\{ \begin{array}{l}
\frac{{ - b}}{{2a}} = \frac{4}{{2a}} = 2\\
9a - 4.3 + c = 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = 1\\
9a + c = 12
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = 1\\
c = 3
\end{array} \right.\\
\Rightarrow y = {x^2} - 4x + 3
\end{array}$
(trục đối xứng chính là hoành độ của đỉnh Parabol)
