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

Nov 28, 2017

See below.

#### Explanation:

Amplitude:

Found right in the equation the first number:

$y = - \underline{2} \cos 2 \left(x + 4\right) - 1$

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:

$y = - 2 \cos \underline{2} \left(x + 4\right) - 1$

Then use this equation:

$p e r i o d = \frac{2 \pi}{k}$

$p e r i o d = \frac{2 \pi}{2}$

$p e r i o d = \pi$

Phase Shift:

$y = - 2 \cos 2 \left(x + \underline{4}\right) - 1$

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

Vertical Translation:

$y = - 2 \cos 2 \left(x + 4\right) \underline{- 1}$

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