How do you determine the amplitude, period, and shifts to graph y = - cos (2x - pi) + 1?

1 Answer
Lydia
Mar 17, 2016

The amplitude is -1, the period is pi, and the graph is shifted to the right pi/2and up 1.

Explanation:

The general pattern for a cosine function would be y=acosb(x-h)+k. In this case, a is -1.

To find the period of the graph, we must find the value of b first. In this case, we have to factor out the 2, in order to isolate x (to create the (x-h)). After factoring out the 2 from (2x-pi), we get 2(x-pi/2).
The equation now looks like this:
y=-cos2(x-pi/2)+1
We can now clearly see that the value of b is 2.
To find the period, we divide (2pi)/b.
(2pi)/b=(2pi)/2=pi

Next, the h value is how much the graph is shifted horizontally, and the k value is how much the graph is shifted vertically. In this case, the h value is pi/2, and the k value is 1. Therefore, the graph is shifted to the right pi/2, and upwards 1.

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