# 10.6: The Discriminant

Difficulty Level:

**At Grade**Created by: CK-12## Learning Objectives

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.

## Vocabulary

Terms introduced in this lesson:

- discriminant
- double root
- nature of solutions
- distinct real solutions
- non-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.

## Error Troubleshooting

General Tip: Remind students to use care when substituting values into the discriminant.

### Image Attributions

## Description

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## Tags:

Activities
Answer Key
Answers
(45 more)
Assessment
CK.MAT.ENG.TE.1.Algebra-I.10
Common Misconceptions
completing the square
Concept Check and Troubleshooting
Differentiated Instruction
discriminant
double root
Enrichment
Inquiry Process
intercept form
line of symmetry
linear functions
linear regression
no real solutions
Pacing
parabolas
perfect squares
Problem Sets
Problem Solving
Pythagorean theorem
quadratic equation
quadratic equations
quadratic function
quadratic functions
quadratic regression
Quizzes
roots
scatter plot
Science Inquiry
Solution Key
Solutions
square roots
standard form
symmetric
Teacher Edition
Teaching Strategies
Teaching Strategies and Tips
Testing
Tests
vertex form
Worksheets
x-intercept
y-intercept
zeroes

## Subjects:

## Date Created:

Feb 22, 2012## Last Modified:

Aug 22, 2014
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