# How do you graph #y=3 sin (2x-pi) + 2#?

##### 1 Answer

graph{y=3sin(2x-pi)+2 [-10, 10, -5, 5]} Use the rules of graphing sine equations.

#### Explanation:

The things that you need to find are the amplitude, the period length, the phase shift, and the amount that it is shifted up or down. The amplitude is represented as A. The period length is the general period of

However, C can be and commonly is moved to the end, making it look like this:

This does not change the application of C.

So, to apply this knowledge, you have to understand what each of those means. The amplitude is how far off of the midline of the graph it rises and falls. Technically, it's the absolute value of A, but whether A is positive or negative determines whether you go down first or up first. So, in this case, your amplitude is 3.

The phase shift is how far to the left or right you move the graph. As it is represented by

The period length is how far one period, or one sine wave, goes. A natural period length is

The vertical shift moves the midline of the graph up or down, depending on whether it is positive or negative. In this case, your