Question 224474: In the function f(x) = ax2 + bx + c, the minimum or maximum value occurs where x is equal to -b/(2a). How is that value derived?
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! This  comes from the quadratic formula. If you solve the quadratic equation  , you get the quadratic formula  . If the radicand (i.e., what is inside the radical!) is equal to ZERO, something special happens, and you get  , so  .
In the same way, the vertex of the quadratic function  occurs at the value where you ZERO out the radical part of the quadratic formula  . As before, this happens when  , and this value of x corresponds to the vertex of the quadratic function. This is the value of x that gives the maximum or minimum value of f(x).
There is a LOT more to say about this, but I've really tried to keep it simple. Even so, this may have been unusually difficult to understand, and if so, I'll have to apologize! I guess I just haven't found a better way to explain it!
R^2
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Campus
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