2014-I-13

$\begin{array}{rcl}
f(2) & = & 59 \\
k_1(2)^2 + k_2 & = & 59 \\
4k_1 + k_2 & = & 59 \ldots \unicode{x2460}
\end{array}$

另外，

$\begin{array}{rcl}
f(7) & = & -121 \\
k_1 (7)^2 +k_2 & = & -121 \\
49k_1 +k_2 & = & -121 \ldots \unicode{x2461}
\end{array}$

$\unicode{x2461} – \unicode{x2460}$，可得

$\begin{array}{rcl}
45k_1 & = & -180 \\
k_1 & = & -4
\end{array}$

把 $k_1=-4$ 代入 $\unicode{x2460}$，可得

$\begin{array}{rcl}
4(-4) + k_2 & = & 59 \\
k_2 & = & 75
\end{array}$

$\therefore f(x)= -4x^2 + 75$。由此，可得

$\begin{array}{rcl}
f(6) & = & -4(6)^2 + 75\\
& = & -69
\end{array}$

$\begin{array}{cl}
= & 2 \times 69 \\
= & 138
\end{array}$

留意 $AB$ 為一水平線。所以 $\Delta ABC$ 的高度

$\begin{array}{cl}
= & 6- 0 \\
= & 6
\end{array}$

由此，$\Delta ABC$ 的面積

$\begin{array}{cl}
= & \dfrac{1}{2} \times 138 \times 6 \\
= & 414
\end{array}$