Given the expression: -x^2+18x-99 to solve by completing squares we proceed as follows: -x^2+18x-99=0 this can be written as: -x^2+18x=99 x^2-18x=-99.......i but c=(-b/2)² Hence: c=(-(-18)/2)²=81 adding 81 in both sides of i we get: x^2-18x+81=-99+81 factorizing the quadratic we obtain: (x-9)(x-9)=-18 thus (x-9)²+18=0 the above takes the vertex form of : y=(x-k)²+h where (k,x) is the vertex: the vertex of our expression is: (9,18) hence the maximum point is at (9,18) NOTE: The vertex gives the maximum point because, from the expression we see that the coefficient of the term that has the highest degree is a negative, and since our polynomial is a quadratic expression then our graph will face down, and this will make the vertex the maximum point.
