Learning Resources
Lesson
During this lesson you will be exposed to different methods for solving quadratic equations which produce the same results. Depending on the precision of results required, you will discover that some methods for finding roots are more accurate than others.
As you progress through this focus make note of the items called Reflections in the sidebar of your text book; these items give valuable pointers that will help in your calculations.
Read and study the introduction and the Focus (p.41) . Answer the focus questions. If you have any problems or difficulties following the steps provided go to the next page for comments and hints.
Method 1 : Graphing
Click here and follow the steps to find the zeros of the function from a graph using CALC with the ZERO command on the TI - 83.
Method 2 : Factoring using Algebra Tiles
The use of algebra tiles are efficient when they are used to form a square or rectangle with numbers that are not very large. However, when the values are decimals or fractions the tiles are not very useful. Recall your experiences with these tiles from earlier mathematics courses and follow the reasoning provided; however, you will not have to use this method very often, if at all. The Note in the side bar for this method is very important since the zero product principle is the key to finding the roots of the equation.
Method 3 : Factoring by Decomposition
If 
in the quadratic equation, then the factoring process or the patterns for factoring may not be obvious. A process known as decomposition can be used to factor the quadratic expression. Click here to see another example.
You should write a journal entry explaining how this is done using an example of your own.
Method 4 : Completing the square
Draw a connection here with the process developed in section 1.3 - it is almost the same except in place of y you have 0 (i.e. instead of 
we have 
). The process of completing the square is essentially the same.
Make note in this solution that the square root of a number produces two solutions, one positive and one negative. These solutions must be interpreted in terms of the problem; for example, the negative answer may not make sense for the situation and becomes what is known as as inadmissible root or extraneous root ( for example distance and time are not negative.)
You should realize by now that zeros of a function, x-intercepts of a graph and roots of an equation are essentially the same. Explain to your own satisfaction.
Activity
Focus Questions p.43 - 44. Complete 1 to 7 inclusive
Think About p.41, p.42 and p.43
Challenge Yourself p.45 and p.47
Check Your Understanding p.44 - 47. Complete 8 to 22 inclusive
When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.
After you do the assigned activities, continue on the Test Yourself section for a quick quiz on this lesson.
Test Yourself
The Port aux Basques Recreation Commission plans to add a swimming pool onto its sports complex and at the same time widen the existing arena. If the present arena is 30 meters by 20 meters and its area is doubled by adding a strip at one end and a strip with the same width along one side, find the width of the strip required?