question 23 1 pts given y = -3 sin(π/4 x + π/2) + 2, find the amplitude, period, phase shift and vertical…

Answer:

B. 3; 8; -2; 2

Explanation:

Step1: Find the amplitude

The amplitude of $y = A\sin(Bx - C)+D$ is $|A|$. For $y=-3\sin(\frac{\pi}{4}x+\frac{\pi}{2}) + 2$, $A=-3$, so amplitude $|A| = 3$.

Step2: Calculate the period

The period formula is $T=\frac{2\pi}{|B|}$. Here $B = \frac{\pi}{4}$, so $T=\frac{2\pi}{\frac{\pi}{4}}=8$.

Step3: Determine the phase - shift

The phase - shift formula is $\frac{C}{B}$. Rewrite $y=-3\sin(\frac{\pi}{4}x+\frac{\pi}{2}) + 2$ as $y=-3\sin(\frac{\pi}{4}(x + 2))+2$. The phase - shift is $\frac{-\frac{\pi}{2}}{\frac{\pi}{4}}=- 2$.

Step4: Identify the vertical shift

For the function $y = A\sin(Bx - C)+D$, the vertical shift is $D$. Here $D = 2$.