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

1 Answer
Nov 27, 2017

Answer:

First factor, then pick apart the equation.

Explanation:

Factor out #(2x-pi)# to get #2(x-pi/2)#.

Then, before analyzing the equation, draw the root equation which is #y=cosx#

Now start picking out the important stuff.

Amplitude :
a in the equation.

#y=ul2cos(2(x-pi/2))+2#

The amplitude of 2 will stretch #y=cosx# by a factor of 2.

Period :
Find the period by looking at the second 2 in the equation.

#y=2cos(ul2(x-pi/2))+2#

Now calculate period:
#period=(2pi)/k#

#period=(2pi)/2#

#period= pi#

Apply this to your graph, which will compress it from a period of #2pi# to now just #pi#. (Also can be seen as horizontal compression by factor of #1/2#)

Translations :
The last 2 parts of graphing is the translations.

#y=2cos(2(x-ul(pi/2)))+ul2#

The first translation is a horizontal translation right #pi/2# units. So move the graph right #pi/2#.
The second translation is a vertical translation up 2 units. Finally, move graph up 2 units.

If you think you may still have it wrong, refer to this handy tool for checking: https://www.desmos.com/calculator

Voila! All done!
Please correct me if I am wrong!