Question 571016
According to Physics, the height as a function of time in seconds should be
{{{h(t)=-16t^2+96t+256}}}
After 3 seconds, the object's height is
{{{h(3)=-16*3^2+96*3+256}}}
{{{h(3)=-16*9+288+256}}}
{{{h(3)=-144+288+256}}}
{{{h(3)=400}}}
The quadratic function {{{h(t)}}} has a maximum and its graph (h versus t) is a parabola.
To figure out when it reaches its highest altitude, find the axis of symmetry of the parabola:
{{{x=-288/(2*(-16))}}} --> {{{x=9}}}
So the object reaches its maximum height at 9 seconds.
That height is {{{h(9)=-16*9^2+96*9+256}}}
To find out when it hits the ground ({{{h(t)=0}}}), you solve the quadratic equation
{{{-16t^2+96t+256=0}}} or the equivalent {{{16t^2-96t-256=0}}}