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

1 Answer
Nov 28, 2017

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.