You are knitting a blanket. you want the area of the planet to be 24ft^2. you want the length of the blanket to be 2ft longer than it's worth. what should the dimensions of the blanket be?

The area of the blanket - 24 ft²
length being longer than the width means that blanket is a rectangle 
width of the blanket = x 
length of blanket = x +2
area = length * width 
area = x * (x+2)
        = x² + 2x
since area = 24
x² + 2x = 24
x² + 2x - 24 = 0
we have a quadratic equation and we need to now solve for x
x² + 6x - 4x - 24 = 0
x (x + 6) - 4(x + 6) = 0
(x-4) (x+6) = 0
x-4 = 0    or x + 6 = 0
x = 4      or x = -6
x could be either 4 or -6. since dimensions cannot have negative values,
x ≠ -6
therefore x = 4
width = 4 ft
length = 6 ft 

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.