Question #e7f98

1 Answer
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