Question 636699
{{{ f(x) = -2x^2 + 2x + 6 }}}
{{{ f(x) = a*x^2 + b*x + c }}}
{{{ a = -2 }}}
{{{ b = 2 }}}
{{{ c = 6 }}}
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{{{ -b / (2a) = -2/(2*(-2)) }}}
{{{ -b / (2a) = 1/2 }}}
{{{ x[max] = 1/2 }}}
Now plug this back into equation
{{{ f(1/2) = -2*(1/2)^2 + 2*(1/2) + 6 }}}
{{{ f(1/2) = -1/2 + 1 + 6 }}}
{{{ f(1/2) = 13/2 }}}
This is y-co-ordinate of vertex
There is a maximum at ( 1/2. 13/2 )
{{{ x = 1/2 }}} is equation of line of symmetry
{{{ y[max] = 13/2 }}}
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Here's the plot:
{{{ graph( 400, 400, -5, 5, -5, 10, -2x^2 + 2x + 6 ) }}}