Question 1094691
{{{ y = (-1/6)*x^2 - (1/3)*x + 8 }}}
The x-value of the vertex 
( maximum or minimum ) is at:
{{{ -b/(2a) }}}
{{{ a = -1/6 }}}
{{{ b = -1/3 }}}
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{{{ -b/(2a) = (1/3) / ( -1/3) }}}
{{{ x[v] = -1 }}}
plug this value back into equation
{{{ y[v] = (-1/6)*(-1)^2 - (1/3)*(-1) + 8 }}}
{{{ y[v] = -1/6 + 1/3 + 8 }}}
{{{ y[v] = 1/6 + 48/6 }}}
{{{ y[v] = 49/6 }}}
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The vertex is at ( -1, 49/6 )
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Here's the plot:
{{{ graph( 400,400, -9, 7, -2, 10, (-1/6)*x^2 - (1/3)*x + 8 ) }}}