Precalculus (6th Edition) Blitzer

$$y=-2 \sin 2x$$
Looking at the graph, we find that this is the reflected graph of a sine function about the $x$-axis with amplitude $2$ and period $\pi$. So, we conclude that $$A=2, \quad B=\frac{2\pi }{\pi }=2 \\ \Rightarrow \quad y=-A \sin Bx = -2 \sin 2x.$$