POINT OF INTEREST

Copyright by Ingrid Stewart, Ph.D.  Please Send Questions and Comments to ingrid.stewart@csn.edu.

Given the General Form of the quadratic equation, the vertex point is .

Proof:

When changing the General Form to Standard Form using the Completion of Squares Method, we get .

Now, if we will let , thenequals 0 and , right?

For any other value of x, the expressionis not equal to 0, right? Then, when added to , it would make all y = f(x) larger (if the leading coefficient a is positive, parabola open up) or smaller (if the leading coefficient a is negative), parabolaa open down) than . 

Therefore must be the minimum or maximum value for all x.