Answer:
(a variation of) vertex form
Step-by-step explanation:
For vertical scale factor "a" and vertex (h, k), the vertex form of the equation for a parabola can be written as ...
y = a(x -h)^2 +k
If k is subtracted from this equation, an alternate form is ...
y -k = a(x -h)^2
This latter version of vertex form is the form your equation has, where ...
Explanation:
The general template of a sine function is
y = Asin(B(x-C))+D
The value of B is the only thing that determines the period T. We ignore every other term.
It turns out that T = 2pi/B which can be solved to B = 2pi/T
Plug in the given period of T = 8pi and compute to get
B = 2pi/T
B = (2pi)/(8pi)
B = 2/8
B = 1/4
This means that the term out front of the x is 1/4 and the equation must be which matches with answer choice B.
