Question 181630
{{{S(t) = -16t^2 + 128t}}}
With a parabola, the maximum or minimum occurs wher
{{{t = (-b)/(2a)}}} when the general formula is
{{{S(t) = at^2 + bt + c}}}
{{{a = -16}}}
{{{b = 128}}}
{{{(-b)/(2a) = (-128)/(2*(-16))}}}
{{{(-b)/(2a) = 4}}}sec
In 4 sec the rocket will reach it's maximum altitude
{{{S(t) = -16t^2 + 128t}}}
{{{S(4) = -16*4^2 + 128*4}}}
{{{S(4) = -128 + 128*4}}}
{{{S(4) = 384}}} ft
The maximum altitude is 384 ft