1. Lesson 3

1.6. Explore 2

Mathematics 20-1 Module 3

Module 3: Quadratic Functions

 

Completing the Square Using Only Algebra

 

You are ready to learn to complete the square for a quadratic function in standard form using only algebra. While algebra tiles are your best bet if you need a good visual of what is happening to the equation as you complete the square, completing the square using only algebra is faster and easier.

 

Completing the square using algebra will enable you to convert the standard form of the quadratic function, y = ax2 + bx + c, to the vertex form, y = a(x − p)2 + q.

 

This is an illustration that shows that the standard form will be converted to the vertex form.

 

Example 1: Completing the Square

 

Complete the square to convert the following quadratic function to vertex form.

 

 



textbook
Sometimes there is a coefficient in front of the x2-term. Look at a couple of examples of how this is handled on page 186 of the textbook. Begin at “Method 2: Use an Algebraic Method.” Note how the square brackets are used to keep track of the values multiplied by the coefficient of the x2-term.


caution

Be careful when converting to the vertex form of a quadratic equation. One of the most common mistakes students make is that they forget to calculate the sign (+ or −) of the coefficients when working with brackets.

 

It is important that you always include the sign and the value of the coefficients in front of a bracket when you put numbers into a bracket or remove numbers from the bracket.

 

Watch Animated Example 1: Completing the Square and Animated Example 2: Completing the Square. Pay special attention to the signs and the use of brackets in each case. Note the subtle difference between these examples.

 

 
This is a play button that opens Animated Example 1: Completing the Square.
 
This is a play button that opens Animated Example 2: Completing the Square.