1. Lesson 3

1.11. Lesson 3 Summary

Mathematics 20-1 Module 4

Module 4: Quadratic Equations and Inequalities

 

Lesson 3 Summary

 

This shows a photo collage of pruned shrubs. In the photo on the left, the shrubs are shaped to look like a unicorn and a bear.

first hedge: © psnoonan/23693382/Fotolia; second hedge: © brozova/24543439/Fotolia



In this lesson you investigated the following questions:

  • In what circumstances would completing the square be favourable over other strategies for solving quadratic equations?

  • What is the goal of completing the square and how does this help determine the roots of a quadratic equation?

You learned how to determine the roots of a quadratic equation by completing the square. You discovered that, just as you did with quadratic functions, you can convert a quadratic equation in standard form to the form a(x − p)2 + q = 0 by completing the square. This form is used to solve the equation for its roots. The key is to isolate the binomial square and then to take the square roots of each side of the equation. This quickly leads to the isolation of x and the determination of the roots as either exact or approximate values.

 

Solving a quadratic equation by completing the square has several advantages over the other methods:

  • Since the method is an algebraic method, completing the square can show the mathematical principles underlying the solution.

  • This method can provide an exact value, whereas graphing methods may not.

  • This method helps you solve equations that are not easily factored.
In the next lesson you will use the method of completing the square to develop a formula that can be applied to the solutions of all quadratic equations. You will also analyze the formula to determine the nature of the roots of any quadratic equation.