Question 811813
Since this is a parabola, there will likely
be 2 solutions. One solution is the time 
when the object is on it's way up and reaches
120 ft. The other solution is the time when
the object is on it's way down and reaches
120 ft again.
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{{{ h(t) = -16t^2 + 64t + 8 }}}
( actually, it looks like the 8 should be a 12,
which is the initial height, but I'll leave it 8 )
{{{ h(t) = 120 }}}
{{{ 120 = -16t^2 + 64t + 8 }}}
{{{ -16t^2 + 64t - 112 = 0 }}}
{{{ -t^2 + 4t - 7 = 0 }}}
I'll complete the square
{{{ -t^2 + 4t = 7 }}}
{{{ t^2 - 4t = -7
{{{ t^2 - 4t + (4/2)^2 = -7 + (4/2)^2 }}}
{{{ t^2 - 4t + 4 = -3 }}}
{{{ ( t - 2 )^2 = -3 }}}
Both sides need to be a perfect square for this
to work, and {{{-3}}} is not a square of anything.
I don't think the object ever reaches 120 ft
Here's a plot:
{{{ graph( 400, 400, -1, 6, -10, 100, -16x^2 + 64x + 8 ) }}}
It looks like it's maximum height is 72 ft at 2 sec
Is something copied wrong?
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Note:  it's = it is