Question 840522
The formula for the vertex ( or peak ) is
{{{ t[max] = -b/(2a) }}}
{{{ a = -16 }}}
{{{ b = 96 }}}
{{{ t[max] = -96/(2*(-16)) }}}
{{{ t[max] = 3 }}}
Now plug the value of {{{ t[max] }}} back
into the equation to find {{{ s[max] }}}
{{{ s[max] = -16*3^2 + 96*3 + 120 }}}
{{{ s[max] = -144 + 288 + 120 }}}
{{{ s[max] = 264 }}}
(a)
The max distance above ground is 264 ft
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To find the height of the building, set {{{ t=0 }}}
{{{ s(0) = -16*0^2 + 96*0 + 120 }}}
{{{ s(0) = 120 }}}
(b)
the height of the building is 120 ft
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Here's the plot:
{{{ graph( 400, 400, -1, 8, -30, 300, -16x^2 + 96x + 120 ) }}}