Question 1033705
{{{ f(x) = x^2 - 9x + 14 }}}
The vertex ( either maximum or minimum )
is at {{{ x[v] = -b/(2a) }}} when the form is:
{{{ a*x^2 + b*x + c }}}
{{{ a = 1 }}}
{{{ b = -9 }}}
{{{ x[v] = -(-9) / ( 2*1 ) }}}
{{{ x[v] = 9/2 }}}
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Another way to see this is: the vertex is midway
between the roots
{{{ f(x) = 0 }}}
{{{ f(x) = ( x-7 )*( x-2 ) }}}
{{{ x = 7 }}}
{{{ x = 2 }}}
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The midway point is at:
{{{ x[v] = ( 7 + 2 ) / 2 }}}
{{{ x[v] = 9/2 }}}
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Plug this value back into equation
{{{ f(9/2) = (9/2)^2 - 9*(9/2) + 14 }}}
{{{ f(9/2) = 81/4 - 81/2 + 14 }}}
{{{ f(9/2) = 81/4 - 162/4 + 56/4 }}}
{{{ f(9/2) = -25/4 }}}
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The vertex is at ( 9/2, -25/4 ), which means it must be 
a minimum since there are 2 roots on either side  which
are above the vertex.
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Here's the plot:
{{{ graph( 400, 400, -2, 10, -8, 10, x^2 - 9x + 14  ) }}}