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Below is the graph of y = acos(bx+c)+d, where a, b, and c are positive, and c is as small as possible. Find a + b + c+d.

 Oct 28, 2019
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The graph of cos is shifted up (by d)   , shifted RIGHT (to make c as small as possible ----- c will be NEGATIVE) and amplified (by a)  and period is increased to 3pi (from normal 2pi)

 

Amplification   'a'    Normal cosine is from -1 to 1  ( amplitude = 1)   this graph is from -1 to 3  (amplitude = 2)    so  a = 2

 

Period is changed by b    = 2/3

shifted LEFT by 3pi/2 (to make c as small as possible, but still positive) but multiplied by 2/3 (above) makes it just pi   pi = c

And finally ....shifted UP  from midline = 0 to midline = 1       1 = d

 

 

Here is a graph:

https://www.desmos.com/calculator/rpslirnhyi

 

 

( RED text is edited/corrected text....THANX to CPhil !)

 Oct 28, 2019
edited by ElectricPavlov  Oct 28, 2019
edited by ElectricPavlov  Oct 29, 2019

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