Question 201852
First, it appears as though that you have a little mix-up in the independent variable (t) in the formula.  It should be:
{{{S(t) = -16t^2-32t+128}}}
A) What is the height of the wrench after 1 second?
Set t = 1 and solve for S.
{{{S(1) = -16(1)^2-32(1)+128}}}
{{{S(1) = -16-32+128}}}
{{{S(1) = -48+128}}}
{{{highlight(S(1) = 80)}}}feet.
B) How long does it take for the wrench to reach the ground?
Here, you are looking for the time, t, at which S(t) is zero (ground-level), so set S(t) = 0 and solve for t.
{{{-16t^2-32t+128 = 0}}} To simplify the calculations a bit, divide both sides by -16.
{{{t^2+2t-8 = 0}}} Factor the trinomial.
{{{(t+4)(t-2) = 0}}} Now apply the zero product rule.
{{{t+4 = 0}}} or {{{t-2 = 0}}} so then...
{{{t = -4}}} or {{{t = 2}}} Discard the negative solution as time is a positive value.
{{{highlight(t = 2)}}}seconds.