Question 114519
Please read my lesson---Shortcut in finding the vertex of any parabola

IF {{{y=-x^2+4x-9}}}, then {{{dy/(dx)=-2x+4}}}


Equating to zero,

{{{-2x+4=0}}}
{{{-2x=-4}}}
{{{x=1/2}}}

Solving for y,

{{{y=-(1/2)^2+4(1/2)-9=-31/4}}}


Thus, the vertex is at ({{{1/2)}}},{{{-31/4}}})


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HyperBrain!