# Question #e7f98

Dec 15, 2017

y = 3(1/4(x - 3$\pi$/2)) - 4

#### Explanation:

Consider this skeleton equation:
y = a(bx + c) + d

Amplitude is the a value, so plug it in for a in the equation:
y = 3(bx + c) + d

With the period you can find the b value using this equation:
period = 2$\pi$/b
(use 2$\pi$ for cos,sin,csc,sec functions & just $\pi$ for tan,cot fucntions)
Since you already know the period, plug it in to this equation and solve for b:
8$\pi$ = 2$\pi$/b ---> b = 1/4
Now plug this b value into the skeleton equation:
y = 3(1/4(x + c)) + d

Phase shift of 3$\pi$/2 means the graph shifts left, so it's the c value; now plug it into the equation:
y = 3(1/4(x - 3$\pi$/2)) + d

Finally, the vertical shift of -4 is shifting the graph downward, which is the d value. Now plug it into the equation to get the final equation:
y = 3(1/4(x - 3$\pi$/2)) - 4