find the phase shift, amplitude, and period o...

# Explanation: ## Step1: Recall the general form of a sinusoidal function The general form of a sinusoidal function is $y = A\sin(Bx - C)+D$. For the given function $y=-2 + 3\sin(3x+\frac{\pi}{4})$, we can rewrite it as $y = 3\sin(3x+\frac{\pi}{4})-2$, where $A = 3$, $B = 3$, $C=-\frac{\pi}{4}$, and $D=-2$. ## Step2: Calculate the amplitude The amplitude of a sinusoidal function $y = A\sin(Bx - C)+D$ is given by $|A|$. Since $A = 3$, the amplitude is $|3|=3$. ## Step3: Calculate the phase - shift The phase - shift of a sinusoidal function $y = A\sin(Bx - C)+D$ is given by $\frac{C}{B}$. Here, $C =-\frac{\pi}{4}$ and $B = 3$, so the phase - shift is $\frac{-\frac{\pi}{4}}{3}=-\frac{\pi}{12}$. ## Step4: Calculate the period The period of a sinusoidal function $y = A\sin(Bx - C)+D$ is given by $\frac{2\pi}{|B|}$. Since $B = 3$, the period is $\frac{2\pi}{3}$. # Answer: Phase shift: $-\frac{\pi}{12}$ Amplitude: $3$ Period: $\frac{2\pi}{3}$