Lesson 3

 

Lesson 3: Solving Quadratic Equations by Completing the Square

 

Focus

 

 

Have you ever seen a beautiful building? You may have travelled to places and seen immense structures with strange but appealing designs. You may have some beautiful buildings in your own community. Consider the photos shown. What is the difference between each sketch and its accompanying photo? Does the absence of landscape features in the sketches add to, or subtract from, the beauty of the buildings?

 

Landscaping is an important part of beautifying an area, especially the grounds of important buildings such as the Taj Mahal in Agra, India. Landscape design and landscape architecture are both professions that deal with the design and development of public spaces to meet minimum standards of beauty, practicality, and environmental impact.

 

In this lesson you will learn how to solve quadratic equations by completing the square. You will investigate problems related to landscape design that can be modelled and solved using quadratic equations.

 

Outcomes

 

At the end of this lesson, you will be able to

• solve a quadratic equation of the form ax2 + bx + c = 0 by determining square roots
  
  
• solve a quadratic equation of the form ax2 + bx + c = 0 by completing the square

Lesson Questions

 

You will investigate 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?

Assessment

Your assessment may be based on a combination of the following tasks:

• completion of the Lesson 3 Assignment (Download the Lesson 3 Assignment and save it in your course folder now.)
  
  
• course folder submissions from Try This and Share activities
  
  
• additions to Module 4 Glossary Terms and Formula Sheet
  
  
• work under Project Connection