# What is the amplitude, period, phase shift and vertical displacement of y=2sin(2x-4)-1?

Feb 20, 2018

See below.

#### Explanation:

When $y = a \sin \left(b x + c\right) + d$,

amplitude = $| a |$
period = $\frac{2 \pi}{b}$
phase shift = $- \frac{c}{b}$
vertical shift = $d$

(This list is the kind of thing that you have to memorize.)

Therefore, when $y = 2 \sin \left(2 x - 4\right) - 1$,

amplitude = 2
period = $\frac{2 \pi}{2}$ = $\pi$
phase shift = $- \left(- \frac{4}{2}\right)$ = 2
vertical shift = -1