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

Given the

General Formof the quadratic equation, the vertex point is.Proof:

When changing the

General FormtoStandard Formusing theCompletion of Squares Method, we get .Now, if we will let , thenequals

0and , right?For any other value of

, the expressionis not equal to 0, right? Then, when added to , it would make allxlarger (if the leading coefficienty = f(x)is positive, parabola open up) or smaller (if the leading coefficientais negative), parabolaa open down) than .aTherefore must be the minimum or maximum value for all

.x