Example 1 (Shandong) Let the line $l$ with a slope of 2 pass through the focus $F$ of the parabola $y^{2}=$ $a x(a \neq 0)$, and intersect the $y$-axis at point $A$. If the area of $\triangle O A F$ (where $O$ is the origin) is 4, then the equation of the parabola is ( ).
A. $y^{2}= \pm 4 x$
B. $y^{2}= \pm 8 x$
C. $y^{2}=4 x$
D. $y^{2}=8 x$
Explain that for the parabola $y^{2}=a x(a \neq 0)$, the coordinates of the focus $F$ are $\left(\frac{a}{4}, 0\right)$. Therefore, the equation of the line $l$ is $y=2\left(x-\frac{a}{4}\right)$, and its intersection with the $y$-axis is $A\left(0,-\frac{a}{2}\right)$. Thus, the area of $\triangle O A F$ is $\frac{1}{2}$ $\left|\frac{a}{4}\right| \cdot\left|\frac{a}{2}\right|=4$, solving for $a$ gives $a= \pm 8$. Hence, the equation of the parabola is $y^{2}=$ $\pm 8 x$. Choose B.