7. Given that the line $y=-2 x+3$ intersects the parabola $y=$ $x^{2}$ at points $A$ and $B$, and $O$ is the origin. Then, the area of $\triangle O A B$ is $\qquad$ .
7.6 .

As shown in the figure, the line $y=$
$-2 x+3$ intersects the parabola $y$ $=x^{2}$ at points $A(1,1), B(-3,9)$.
Construct $A A_{1}, B B_{1}$ perpendicular to the $x$-axis, with feet of the perpendiculars at
$$
\begin{array}{l}
A_{1} 、 B_{1} . \\
\therefore S_{\triangle O A B}=S_{\text {trapezoid } A A_{1} B_{1} B}-S_{\triangle A A_{1} O}-S_{\triangle B B_{1} O} O \\
=\frac{1}{2} \times(1+9) \times(1+3)-\frac{1}{2} \times 1 \times 1 \\
\quad-\frac{1}{2} \times 9 \times 3=6 .
\end{array}
$$