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