How would you find the maximum point on a quadratic graph?

If you are finding a maximum point on a quadratic graph, then note firstly the coefficient of x^2 must be negative.

The most sound method to determine the maximum is to find the point where dy/dx = 0. If y = ax^2 + bx + c. Then dy/dx = 2ax+b. If dy/dx = 0, then 2ax + b = 0; therefore x = -(b/2a). The maximum point on the quadratic graph would be where x = -(b/2a) given that a<0.