At the end of this lesson, students will be able to:
- Find the discriminant of a quadratic equation.
- Interpret the discriminant of a quadratic equation.
- Solve real-world problems using quadratic functions and interpreting the discriminant.
Terms introduced in this lesson:
nature of solutions
distinct real solutions
rational number solutions
irrational number solutions
Teaching Strategies and Tips
In this lesson, students learn that each quadratic equation is associated with a number whose sign tells how many solutions there are to that equation.
- Emphasize that the equation does not have to be solved.
Point out that if the discriminant is not a perfect square, then the solutions are irrational numbers. See Example 3.
Use Examples 5-7 to illustrate how useful interpreting the discriminant in context of the problem can be.
General Tip: Remind students to use care when substituting values into the discriminant.