Session 8 (Week 4b)

Chapter 2 Polynomials

Section 2.4 Solving Quadratic Equations

1. Activities

W. Michael Kelley (2006). The Humongous Book of Calculus Problems.

Complete problems 2.28 - 2.32 [p. 23 - 25]

Wayne W. Dyer (2007). Change Your Thoughts - Change Your Life.

Read Verse 8: Living in the Flow [p. 39 - 43]

2. What's it all about?

This section discusses three different methods for finding the roots of a quadratic equation.

3. What am I able to do, now that I am finished this section?

• solve quadratic equations by factoring
• solve quadratic equations by using the quadratic formula
• solve quadratic equations by completing the square

4. What will I know?

• I should understand the principle underlying each of the three different methods for finding the roots of a quadratic equation.

5. What are the key concepts?

• quadratic equation
• root of an equation
• relationship between a factor and the root of an equation

6. What are some relevant Web sites for this material?

Using your favorite search engine, and maybe one or two others, type in a few key words such as "solving quadratic equations".

Here are a few Web sites that I liked:

• http://www.purplemath.com/modules/solvquad.htm
• http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut17_quad.htm
• http://home.alltel.net/okrebs/page6.html
• http://www.uncwil.edu/courses/mat111hb/Pandr/quadratic/quadratic.html

7. What concept map can I create for this section?

8. What types of Mathematica activities can I create?

Mathematica can find the roots for any quadratic equation by using the command Solve. This should always be supplemented by creating a graph of the function.

9. What are some connections to other ideas?

Note how all three solutions are basically special cases of one general principle, which is to find the two places where the graph of the equation passes through the x-axis. These are the two values where the value of the equation is equal to zero.

The general solution is one derived algebraically, but the formula is cumbersome. If one can find an easier approach (i.e. one where the algebra leads to a simple factor which then means that the root is obvious by inspection).

The word "solve" has many different meanings in mathematics. Solving an equation means finding the roots of the equation.

10. What is my overall reaction to this section?

This is an easy section, with only one idea (but three different strategies) for finding the roots of a quadratic equation.

11. Comments on Dyer: 8. Living in the Flow

Dyer suggests that you should see parallels between water and the way that one conducts one's own life. The basic idea is to go with the flow of the situation. In the case of mathematics, let your mind relax and it will see patterns and paths that lead to understanding and the solution. Do not fight against the problem but let it solve itself.