1. Lesson 4

1.6. Explore 2

Mathematics 20-1 Module 4

Module 4: Quadratic Equations and Inequalities

Developing the Quadratic Formula

 

This is a play button that opens Developing the Quadratic Formula.

You derived the quadratic formula in Try This 1. You will now examine the formula’s development further. Retrieve your work from Try This 1. Open Developing the Quadratic Formula, which shows an approach that may look like the method you used in Try This 1.

 

To get to the applet, select The Quadratic Formula, and then select Developing the Quadratic Formula, under the Tutorial icon. Take your time to fully understand each step.

 

tip bar

It can be confusing to manipulate algebraic expressions that contain multiple variables. A helpful technique is to work through a similar expression but substitute values for the variables a, b, and c. In this case, you could choose a quadratic equation such as 2x2 + 9x – 4 = 0 to solve by completing the square. This way you can see what happens to the numbers at each step.



You have seen that you can determine the roots of any quadratic equation of the form ax2 + bx + c = 0 by using this formula:

 

 

 


formula sheet

Add the quadratic formula to your copy of Formula Sheet.

 

Try This 2

 

Consider the quadratic equation 6x2 − 14x + 8 = 0.

  1. Use the quadratic formula to determine the roots of the equation.

  2. Verify the roots by substituting them, each in turn, into the original equations. Show that by doing so, the expression becomes zero and the equation is satisfied.

  3. What sorts of errors could a person make when using the quadratic formula? List any errors you found in your own work. If you didn’t have any errors, think of some places in the solution process where you would have to be careful.

course folder Save your work in your course folder.


textbook

Turn to “Example 2” on page 248 in the textbook. Work through the solution process for both equations. Pay attention to the differences between the two solutions. The questions in green refer to a discriminant. What do you think the discriminant is?

 

Self-Check 1

 

This is a play button that opens Quadratic Formula Self-Check.

Check your understanding by completing Quadratic Formula Self-Check.

 

 

The discriminant is the resulting value from calculating b2 − 4ac under the radical sign.

This answer is important. Check your answer before moving on. The roots are  and x = 1.


Do your solutions match? If not, review your work to see where you might have made an error. You can turn to page 251 of the textbook to see how this equation can be solved with the quadratic formula. Then return to your original work to make corrections.