I have two questions. A lot of the sources I have read say that amplitude cannot be negative, because it is a distance, and we take the absolute value of distance. However, other sources say that A can be negative (like SymboLab).

My second question is, I have to find a function from its graph:

I

I first calculated the amplitude to be: (Max+Min) / 2 = (2+2) / 2 = 2

The parent function to be: y = a * sin [k (x-d)] + c

The period to be : pi radians

The vertical translation, 'c' to be: 0

The phase shift to be: pi/6, so d = pi/3

However, when I used Desmos to graph the final function: y = 2 sin [2(x-pi/3)], I got the wrong answer. I used trial and error, and flipped it over the x-axis, and then I got the matching function. Why is it a -2 instead of a +2 then? Can anybody please explain this?

Oh yeah, this is what sums up my past three hours trying this.

I actually completed calculus I last semester and I am taking trig again over the summer.