Question 1087720
The equation should be:
{{{ H = -16t^2 + 96t + 6 }}}
( I noted you said at {{{ t=0 }}} the
object was {{{ 6 }}} ft off the ground, 
it should be {{{ 16 }}} ft. )
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{{{ H = -16t^2 + 96t + 16 }}}
{{{ H = 160 }}}
{{{ 160 = -16t^2 + 96t + 16 }}}
{{{ -16t^2 + 96t - 144 }}}
{{{ -t^2 + 6t - 9 = 0 }}}
{{{ ( t - 3 )*( -t + 3 ) = 0 }}}
{{{ t = 3 }}}
The object is at a height of 160 ft
only once, at t = 3 sec
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check:
here's the plot:
{{{ graph( 400, 400, -1, 7, -18, 180, -16x^2 + 96x + 16 ) }}}
My answer looks about right