Question 1025172
{{{ h = -8t^2 + 40t }}}
The x-value of the vertex is at:
{{{ t[v] = -b/(2a) }}} where
{{{ a = -8 }}}
{{{ b = 40 }}}
{{{ t[v] = -40 / ( 2*(-8) ) }}}
{{{ t[v] = 40/16 }}}
{{{ t[v] = 5/2 }}}
Plug this valuie back into the equation
to get {{{ h[v] }}}
{{{ h[v] = -8t^2 + 40t }}}
{{{ h[v] = -8*(5/2)^2 + 40*(5/2) }}}
{{{ h[v] = -8*(25/4) + 200/2 }}}
{{{ h[v] = -50 + 100 }}}
{{{ h[v] = 50 }}}
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It takes 2.5 sec for the ball to reach the highest point
The ordered pair of the vertex point is:
( 2.5, 50 )
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Here's the plot:
{{{ graph( 400, 400, -1, 6, -5, 55, -8x^2 + 40x ) }}}