POINT OF INTEREST

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

Given the Standard Form of the quadratic function, the coordinates of the vertex point (h, k).

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

Proof that .

Let's change the general form of the quadratic function to standard form using the Completing the Square Method.

First, we will factor a out of the general form as follows:

Now we are ready to complete the square.

Please note that we added to complete the square INSIDE the brackets. 

But because of the a outside the brackets, we actually added .  

Therefore, to preserve equality, we must then subtract OUTSIDE the brackets.

Finally, we factor the expression in the brackets to get the standard form of the quadratic function. 

That is, .

Since the standard form is usually written with a minus sign inside the parentheses, we will change the plus sign to as follows:

, where and .