Write an equation of the cosine function with the given amplitude, period, phase shift, and vertical shift. amplitude: 2, period = , phase shift = – , vertical shift = –2

Answer:[tex]y=2\cos(2x+\frac{1}{4})-2[/tex]or[tex]y=-2\cos(2x+\frac{1}{4})-2[/tex]Step-by-step explanation:[tex]y=a cos(c(x-b))+d[/tex] has:1) amplitude=|a|2) phase shift=b3) period=2pi/cd) vertical shift=d--------------------------------------------------You are given the amplitude is 2. This means a could either be 2 or -2.You are given phase shift is -1/8. This means b is -1/8.You are given the period is pi. So we need to solve pi=2pi/c.pi=2pi/cDividing both sides by pi gives:1=2/cMultiply both sides by c gives:c=2The vertical shift is -2 so d=-2.The equation could either be:y=2cos(2(x-(-1/8)))-2ory=-2cos(2(x-(-1/8)))-2Simplifying a little gives:y=2cos(2x+1/4)-2y=-2cos(2x+1/4)-2