How do you work out a quadratic equation with a maximum value?

Alright, so if you have the equation ax^2+bx+c=0, the maximum value is -b/2a for the x value if a is negative, or it's infinity (since the parabola goes on forever). For the y value, simply plug (-b/2a) into the equation. If a is positive, it gives you the minimum value, and if it's negative then it's the maximum. 

Given the maximum value, you know that a is negative, so given the x value of the maximum value you know if b is negative or not. In addition, you can plug numbers in for b and a for what works, as well as having a point from the maximum value to plug in.