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