Question 745110
The maximum height of this parabolic curve is
{{{ s[max] }}} when {{{ t = -b/(2a) }}} and
the equation has the form:
{{{ s(t) = at^2 + b*t + c }}}
In your equation,
{{{ s(t) = -16t^2 + 64t + 50 }}}
{{{ a = -16 }}}
{{{ b = 64 }}}, so
{{{ t = -64 / ( 2*(-16)) }}}
{{{ t = -64 / -32 }}}
{{{ t = 2 }}} sec
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Now find {{{ s(2) }}} which is the maximum height
{{{ s(2) = -16*2^2 + 64*2 + 50 }}}
{{{ s(2) = -64 + 128 + 50 }}}
{{{ s(2) = 114 }}} ft
The maximum height is 114 ft
Here's the plot:
{{{ graph( 400, 400, -2, 5, -10, 130, -16x^2 + 64x + 50 ) }}}