Question

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

Answer 1

See below.

Explanation:

When `y = asin(bx+c)+d`,

amplitude = `|a|`
period = `(2pi)/b`
phase shift = `-c/b`
vertical shift = `d`

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

Therefore, when `y=2sin(2x-4)-1`,

amplitude = 2
period = `(2pi)/2` = `pi`
phase shift = `-(-4/2)` = 2
vertical shift = -1