No, there can not be negative amplitude because it is just the distance between the max and the midline or the minimum and the midline.
I see where you might be confused because for instance in the trig equation:
y = -3 sin (.5(x-

/2)) -1, there is a negative in front of the amplitude. However, when finding the amplitude, you take the absolute value of a.
I guess you mean that the zeroes are 2 and -3/5.
In factor form the function could be
f(x) = (x - 2)(3x + 5)
expanding we get
f(x) = 3x^2 -x - 10