Question 1002955
The formula for the x-coordinate of the vertex is
{{{ x[v] = -b/(2a) }}}
Your equation is:
{{{ h(x) = -(5/6)*x^2 + 20x }}}
{{{ a = -5/6 }}}
{{{ b = 20 }}}
{{{ -b/(2a) = -20/(-10/6) }}}
{{{ -b/(2a) = 20*( 6/10 ) }}}
{{{ -b/(2a) = 12 }}}
Plug this result back into equation to get {{{ h(12) }}}
{{{ h(12) = -(5/6)*12^2 + 20*12 }}}
{{{ h(12) = -(5/6)*144 + 240 }}}
{{{ h(12) = -120 + 240 }}}
{{{ h(12) = 120 }}}
The max height is 120 ft
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The horizontal distance from the launch point will
be double {{{ x[v] }}}
{{{ 2*x[v] = 2*12 }}}
{{{ 2*x[v] = 24 }}}
24 ft
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Here's the plot:
{{{ graph( 400, 400, -3, 30, -20, 140, -(5/6)*x^2 + 20x ) }}}