Question 1157715
{{{ h(t) = -16t^2 + 134t }}}
The vertex ( maximum ) is located midway between
the roots where {{{ h(t) = 0 }}}
{{{ h(t) = t*( -16t + 134 ) }}}
{{{ 0 = t( -16t + 134 ) }}}
the roots are:
{{{ t = 0 }}}
and
{{{ -16t + 134 = 0 }}}
{{{ 16t = 134 }}}
{{{ t = 8.375 }}} sec
-------------------------
{{{ ( 8.375 + 0  ) / 2 = 4.1875 }}}
{{{ t[max] = 4.1875 }}} ( time to reach maximum height )
Plug this back into equation
{{{ h(t) = t*( -16t + 134 ) }}}
{{{ h[max] = 4.1875*( -16*4.1875 + 134 ) }}}
{{{ h[max] = 4.1875*( -67 + 134 ) }}}
{{{ h[max] = 280.56 }}} ft ( maximum height )
check:
Here's the plot:
{{{ graph( 400, 400, -2, 10, -30, 320,  -16x^2 + 134x ) }}}
Looks OK