1. Lesson 4

1.4. Discover

Mathematics 20-1 Module 4

Module 4: Quadratic Equations and Inequalities

 

Discover

 

This shows an “Apple Pi” cartoon strip comprising four panels. In the first panel, one person says to the other: “What you got there?” The second person, who is holding a contraption, replies, “It’s the prototype for a robot I’m designing.” In the second panel, the first person asks, “What does it do?” and the response is, “Everything. It’ll clean my room, put the laundry away, dust, vacuum, answer the phone,..." In the third panel, the first person says, “That’s all? I’ve already got one that’ll do all that and more.” The second person responds, “Really? What’s the robot called?” In the fourth panel, the first person says, “Mom.”

 

Try This 1

 

In this activity you will attempt to derive a formula that can be used to solve a quadratic equation. This formula will be derived by completing the square on the ax2 + bx + c = 0 form of a quadratic equation. You can work alone or with a classmate. It may be easier to work with someone else because you will be able to share ideas and strategies.

  1. The steps to find the exact value of the roots of the equation 2x2 + 3x + 4 = 0 are shown in the left column of the following table. In the right column, determine the exact value of the roots of the general equation ax2 + bx + c = 0 following the same steps used for the specific case. In the general case, you will not be able to simplify numbers since you will be working with unknown quantities. Just focus on the operations and don’t be concerned with the lack of numbers.

     

    Specific Case

    2x2 + 3x + 4 = 0

    General Case

    ax2 + bx + c = 0

     

     

    		  


  2. Look in the textbook or search the Internet for the quadratic formula. Compare the quadratic formula that you find to the roots you found for the general equation in the right column of question 1. Did you obtain the same formula by following the procedure above? If not, explain why not.

course folder Save your work in your course folder.

 

You will have an opportunity to make any necessary revisions later in the lesson.