Question 954466
{{{ s(t) = -16t^2 + 112t + 280 }}}
When the form is:
{{{ y = a*x^2 + b*x + c }}}, then
{{{ x[max] = -b/(2a) }}}
{{{ a = -16 }}}
{{{ b = 112 }}}
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{{{ t[max] = -112/(2*(-16)) }}}
{{{ t[max] = 112/32 }}}
{{{ t[max] = 3.5 }}}
In 3.5 sec, the rocket is at maximum height
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{{{ s(3.5) = -16*3.5^2 + 112*3.5 + 280 }}}
{{{ s(3.5) = -16*12.25 + 392 + 280 }}}
{{{ s(3.5) = -196 + 392 + 280 }}}
{{{ s(3.5) = 476 }}}
The maximum height is 476 ft
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check:
Here's the plot:
{{{ graph( 400, 400, -2, 10, -50, 500, -16x^2 + 112x + 280 ) }}}