Lesson 4

The Value of the Discriminant

Consider the expression underneath the radical in the quadratic formula, b2 − 4ac.

This expression is called the discriminant. In Try This 3 you will see how the value of the discriminant reveals the nature of the roots of the corresponding quadratic equation.

Try This 3

1. Go to Quadratic Equations Table. For each of the equations, evaluate the discriminant. Then sketch the graph of the corresponding quadratic function and insert the graph into the table. Record the number and nature of the roots.
   
   
2. Select several other quadratic equations from the textbook or make some equations up. Determine the discriminant of each of those equations. Sketch the graphs and determine the number and nature of the roots.

Save your work in your course folder.

Share 1

With a classmate, respond to the following questions.

1. What values of the discriminant will result in two real and distinct roots?
   
   
2. What value(s) of the discriminant will result in two real and equal roots?
   
   
3. What values of the discriminant will result in no real roots?
   
   
4. Why do you think the expression b2 − 4ac is called the discriminant?

 Save your work in your course folder.