Question 879538
{{{ h(t) = -16t^2 + 64t }}}
When the form is
{{{ ax^2 + b*x + c }}}, the vertex is
at {{{ t[max] = -b/(2a) }}}
{{{ t[max] = -64/( 2*(-16)) }}}
{{{ t[max] = 2 }}}
Now find {{{ h(2) }}}
{{{ h(2) = -16*2^2 + 64*2 }}}
{{{ h(2) = 64 }}}
The max height is 64 ft
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The rocket hits the ground when {{{ h(t) = 0 }}}
{{{ 0 = -16t^2 + 64t }}}
{{{ 0 = t*( -16t + 64 ) }}}
The rocket hits the ground when 
{{{ -16t + 64 = 0 }}}
{{{ 16t = 64 }}}
{{{ t = 4 }}}
The rocket hits the ground in 4 sec
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Here's the plot:
{{{ graph( 400, 400, -1, 6, -5, 70, -16x^2 + 64x ) }}}