Question 553801
Set h = 96 and solve the quadratic equation for t.
{{{96 = 80t-16t^2}}} Subtract 96 from both sides and rearrange.
{{{16t^2-80t+96 = 0}}} Factor 16 to ease calculations.
{{{16(t^2-5t+6) = 0}}} Factor the trinomial.
{{{t^2-5t+6 = (t-2)(t-3)}}}
{{{(t-2)(t-3) = 0}}} Apply the zero product rule:
{{{t-2 = 0}}} or {{{t-3 = 0}}} so:
{{{t = 2}}} or {{{t = 3}}}
You have two solutions for this problem which was to be expected because quadratics have two solutions.
At t = 2 seconds, the rocket reaches a height of 96 feet on the way up.
At t = 3 seconds, it will pass the 96-foot level on the way down.