Đáp án:
$\begin{array}{l}
\left\{ \begin{array}{l}
f\left( 1 \right) = 2\\
f\left( 3 \right) = 8
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a{.1^2} + b.1 = 2\\
a{.3^2} + b.3 = 8
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a + b = 2\\
9a + 3b = 8
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = 2 - b\\
9.\left( {2 - b} \right) + 3b = 8
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = 2 - b\\
18 - 9b + 3b = 8
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = 2 - b\\
6b = 10
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = 2 - b\\
b = \dfrac{5}{3}
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
a = 2 - \dfrac{5}{3} = \dfrac{1}{3}\\
b = \dfrac{5}{3}
\end{array} \right.\\
Vậy\,a = \dfrac{1}{3};b = \dfrac{5}{3}
\end{array}$
