Question 1051151
{{{ S(t) = -16t^2 + 80t  + 200 }}}
{{{ S(t) = -2t^2 + 10t + 25 }}}
Use the formula for the t-value
of the maximum height
{{{ t[max] = -b/(2a) }}}
{{{ t[max] = -10/(2*(-2)) }}}
{{{t[max] = 5/2 }}}
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Plug this result back into formula to get {{{ S[max] }}}
{{{ S[max] = -16*(5/2)^2 + 80*(5/2) + 200 }}}
{{{ S[max] = -16*( 25/4 ) + 200 + 200 }}}
{{{ S[max] = -100 + 400 }}}
{{{ S[max] = 300 }}}
The maximum height is 300 ft
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Here's the plot:
 {{{ graph( 400, 400, -2, 10, -30, 350, -16x^2 + 80x + 200 ) }}}