Question 553584
Start with:
{{{d = -16t^2-4t+412}}} You are being asked to solve this equation for t when d (distance from the ground) is 400, so you substitute d = 400.
{{{400 = -16t^2-4t+412}}} Subtract 400 from both sides.
{{{0 = -16t^2-4t+12}}} Factor -4 to make it a little easier to solve.
{{{-4(4t^2+t-3) = 0}}} Factor the trinomial.
{{{4t^2+t-3 = (4t-3)(t+1)}}} so now you have:
{{{-4(4t-3)(t+1) = 0}}} Apply the zero product rule.
{{{-4 = 0}}} or {{{4t-3 = 0}}} or {{{t+1 = 0}}}
{{{-4 = 0}}} No way!
{{{4t-3 = 0}}} so {{{4t = 3}}} and {{{t = 3/4}}} or {{{highlight(t = 0.75)}}}
{{{t+1 = 0}}} so {{{t = -1}}} Discard this solution as the time must be a positive quantity.
The rock will be 400 feet from the ground in 0.75 seconds.