Question 203756
Er...what's the question?
Could it be that you want to know when the wrench hits the ground (or an unfortunate passer-by)?
Let's assume that it is!
Given:
{{{S(t) = -16t^2-32t+128}}} the wrench hits the ground when its height, S = 0.
{{{0 = -16t^2-32t+128}}} Rearrange this to look like:
{{{-16t^2-32t+128 = 0}}} Factor out a -16 to ease the calculations a bit.
{{{-16(t^2+2t-8) = 0}}} Note the changes in the signs! Applying the zero product rule, we get:
{{{t^2+2t-8 = 0}}} Factor this quadratic equation.
{{{(t-2)(t+4) = 0}}} from which we get:
{{{t = 2}}} or {{{cross(t = -4)}}} Discard the negative solution as the time, t, should be a positive value.

The wrench hits the ground in 2 seconds.