Question

What is the amplitude, period, phase shift and vertical displacement of `y=-2cos2(x+4)-1`?

Answer 1

See below.

Explanation:

Amplitude:

Found right in the equation the first number:

`y=-ul2cos2(x+4)-1`

You can also calculate it, but this is faster. The negative before the 2 is telling you that there will be a reflection in the x axis.

Period:

First find k in equation:

`y=-2cosul2(x+4)-1`

Then use this equation:

`period=(2pi)/k`

`period= (2pi)/2`

`period= pi`

Phase Shift:

`y=-2cos2(x+ul4)-1`

This part of the equation tells you that the graph will shift left 4 units.

Vertical Translation:

`y=-2cos2(x+4)ul(-1)`

The -1 tells you that the graph will shift 1 unit down.