# How do you graph and list the amplitude, period, phase shift for y=-3sin(2x)-3?

Sep 15, 2016

Amplitude = 3; period = $\pi$, phase shift = 0; vertical shift = $- 3$.

#### Explanation:

In general symbols,

for the oscillation y = a sin (b x +c ) + d,

Amplitude = $| a |$

period = $\frac{2}{b} \pi$

Phase shift = -c/b

Vertical shift = d.

Here, for y = -3 sin (2x) - 3,

Amplitude = 3; period = $\pi$, phase shift = 0; vertical shift = $- 3$.

For the graph, this graph is topsy turvy ( due to negative sign ) of the

graph for

$y = 3 \sin 2 x - 3$

The axis of the wave is $y = - 3$..

One half wave is from (0, -3) to (pi/2, -3),.

with the bisector nadir at (pi/4, -6).

The next half, for one full wave, is from (pi/2, -3) to (pi, -3), with

zenith ( crest ) at (3/4pi, 0).

Now, you can make it for this Table: I lack facility for making it, for

you.

$\left(x , y\right) : \left(0 , - 3\right) \left(\frac{\pi}{4} , - 6\right) \left(\frac{\pi}{2} , - 3\right) \left(\frac{3}{4} \pi , 0\right) \left(\pi , - 3\right)$

Either side outside, it is lateral (horizontal ) successive movement

of this single wave, through the period $\pi$. .