Answer
$y=-2 \sin 2x$
Work Step by Step
Upon inspection, we realize that the graph is an inverted sine function with an amplitude of 2 and a period of $\pi$.
The standard equation $y=a \sin bx$ becomes $y=-a \sin bx$ if the graph is an inverted sin function. In the standard equation $y=a \sin bx$, $a$ is the amplitude. Since the amplitude is 2, a is equal to 2. To find the value of $b$, we use the formula:
Step 1: Period$=\frac{2\pi}{b}$
Step 2: $\pi=\frac{2\pi}{b}$
Step 3: $b=\frac{2\pi}{\pi}$
Step 4: $b=2$
Substituting the values of $a$ and $b$ in the equation $y=-a \sin bx$, we find that the equation of the graph is $y=-2 \sin 2x$.
