# How do you find the amplitude, period, and shift for #f(x) = −4 sin(2x + π) − 5#?

##### 1 Answer

First, let us make this equation in a different format

Only the inside of the sin must change.

We get this to be

Now we have

The amplitude is always the absolute value of the coefficient of sin

This means that the amplitude is

The period can be denoted as

So we have

Now the vertical shift is easy: it is just the D value, which is a vertical shift down by 5 units

The horizontal shift is somewhat tricky. It is related to the C value

Similar to radical functions, this horizontal shift is the opposite of the sign.

For example:

and vice versa

Can you find the horizontal shift after knowing this?

It is a shift to the LEFT by