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y=-x^2+1.5x+2
Find the maximum value.

  • Math -

    If we express the expression in the form of by completing the square:
    y=a(x-h)^2+k
    The maximum k occurs at x=h.

    y=-x^2+1.5x+2
    =-(x-3/4)^2+2+(3/4)^2
    =-(x-3/4)^2+31/16

    Therefore the maximum occurs at x=3/4, the value is 31/16.

    Alternatively, we can solve for the zero in
    y'=0
    and substitute to find the maximum value of y.

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