Precalculus (10th Edition)

$\text{(H)}$
The amplitude and period can be calculated as, if $y=A\sin(wx)$: Amplitude=$|A|$ period: $T=\frac{2\pi}{w}$ In this function, $y=-3\sin(2x)$ Amplitude=$|-3|=3$ Period: $T=\frac{2\pi}{2}=\pi$ Also, the sine function has a $y$-intercept at the origin $y=0$. When $x=\frac{\pi}{4}$, the value of $y$ is $y=-3\sin{\frac{\pi}{4}}$, which is megative. The graph that has the same characteristics is $\text{(H)}$.