Question 906158
The equation should be:
{{{ h(t) = -16t^2 + 68t }}}
The minus sign is for the 
downward pull of gravity
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The formula for {{{ t[max] }}}
is:
{{{ t[max] = -b/(2a) }}}
where:
{{{ a = -16 }}}
{{{ b = 68 }}}
{{{ t[max] = -68/(2*(-16)) }}}
{{{ t[max] = 2.125 }}}
Now find {{{ h[max] }}}
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{{{ h[max] = -16*2.125^2 + 68*2.125 }}}
{{{ h[max] = -72.25 + 144.5 }}}
{{{ h[max] =  72.25 }}}
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The max height is 72.25 ft
when the time is 2.125 sec
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Here's the plot:
{{{ graph( 400, 400, -1, 7, -10, 100, -16x^2 + 68x ) }}}