Lesson 3

1. Lesson 3

1.8. Explore 4

Mathematics 20-1 Module 4

Module 4: Quadratic Equations and Inequalities

Try This 3

Consider the quadratic equation 3x2 – 18x + 7 = 0. (Notice that a = 3.) Complete the steps in Try This 3 Table to determine the roots as exact values. You can print a copy of this table if you prefer.

Save your work in your course folder.

Keep your copy of Try This 3 Table open for the following Share activity.

Share 2

Compare your results with a classmate. Discuss the reasoning for each step. You may want to add a third column, titled “Reasoning,” to your copy of Try This 3 Table. Record the main points of your discussion.

Try solving a similar quadratic equation together.

Save a copy of your discussion in your course folder.

Turn to “Example 3” on page 238 of the textbook to see a slightly different way of solving a quadratic equation of the form ax2 + bx + c = 0, where a ≠ 1. Work through the example to see how this alternate way of completing the square is accomplished. As you do, ask yourself the following questions:

How does the first step in the solution address the issue of a negative value for a? How does this simplify the solution process? How does this step make the solution process more challenging?
How do you enter the exact value in your calculator? Be sure that you use your own calculator to check that you can obtain the same roots as shown in the example.

Self-Check 2

This is a play button that opens Finding the Roots!

Complete Finding the Roots!

You would have to enter the exact values separately as follows:

All of the terms in the equation are divided by −2. This makes factoring easier because you don’t have to worry about dealing with negative factors. This makes the solution process more challenging because factoring the equation now involves fractions.