If you have a trig function $f(x) =- 3\sin (2x) + 1$ then would you ever say that the amplitude is negative? I've seen it stated that it can be negative or that amplitude is a distance so it should only be a positive value. I'm wondering if it depends on the context of the problem. But if I'm talking about a general function with no context, would I always say that the amplitude is positive and then the function is "flipped"?
The amplitude, because otherwise the amplitude would depend on the phase: if you shift the $\sin$ function by $\pi$, it becomes $-\sin$. You don't really want to have what you call the amplitude depend on something as arbitrary as where the function crosses zero. Another example: what would the amplitude of $\sin(x-\pi/4) = -\sin(x+3\pi/4)$ be?
Amplitude is positive as far as I know. its one half the positive difference of the maximum and minimum values. Think of it this way, it is the distance of the maximum and minimum from the Centre axis. For example we have a function $y=-sin(3x)$ the amplitude of this function is amplitude=|a|=|-1|=1. Let me know if you need further help or suggestions.