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

Given the

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

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

Let's change the

general formof the quadratic function tostandard formusing theCompleting the Square Method.First, we will factor

out of theageneral formas 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

aoutside 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 formof the quadratic function.That is, .

Since the

standard formis usually written with a minus sign inside the parentheses, we will change the plus sign to as follows:, where and .