Question

What happens when the a (amplitude) of a sine graph is negative `-2 sin (1/4 x)`?

Answer 1

It simply flips your graph upsidedown. Where it should have a positive amplitude, now gets negative and viceversa:
For example:
if you choose `x=pi` yo get `sin(pi/4)=sqrt(2)/2` but with minus 2 in front your amplitude becomes: `-2sqrt(2)/2=-sqrt(2)`:
Graphically you can see this comparing:
`y=2sin(x/4)`
graph{2sin(x/4) [-11.25, 11.25, -5.625, 5.625]}
with:
`y=-2sin(x/4)`
graph{-2sin(x/4) [-12.66, 12.65, -6.33, 6.33]}