You can put this solution on YOUR website! graph f(x)=-x^2+3x+2 and find the vertex.
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The vertex occurs where x = -b/2a = -3/(2*-1) = 3/2
and f(3/2) = -(3/2)^2+3*(3/2)+2 = -9/4 + 18/4 + 8/4 = 17/4
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Cheers,
Stan H.