<PRE><B>Question 62754</B>

y = - x^2 + 6x

This represents a parabola opening downward and so the vertex will be the maximum point.

The x co-ordinate of the vertex = -b/2a

                                = -6/2*(-1)

                                = -6/-2

                                = 3

Plugging in x = 3 in the given expression,

y = - 3^2 + 6*3

   = -6 + 18

   = 12

Thus the maximum value of y = - x^2 + 6x is 18.

Good Luck!!!</PRE>