Posted by **Kate** on Sunday, July 31, 2011 at 11:13am.

y=-x^2+1.5x+2

Find the maximum value.

- Math -
**MathMate**, Sunday, July 31, 2011 at 11:34am
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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