Education Technology

# Activities

• ##### Subject Area

• Math: Precalculus: Polynomial, Power, and Rational Functions
• Math: College Algebra: Equations and Inequalities

9-12

30 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• TI-Nspire™
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.2

## Discriminating Against the Zero

#### Activity Overview

In this introductory activity, students explore when a graph has two zeros, one zero, and no real zeros. They will also determine when a graph has real, rational, irrational, or imaginary roots. The teacher should then follow up with a formal discussion on the discriminant.

#### Key Steps

• In this activity, students explore the roots or zeros or a quadratic function. They will use sliders to change the value of b and c in the function f(x) = ax2 + bx + c. They will compare the number and type of zeros of the graph to the number under the square root of the quadratic formula. The connections that students make will introduce them to the discriminant.

• After exploring the graph, students will use the quadratic equation to find irrational and imaginary roots. They are to first do it by hand and then check their answers using the handheld.

• The last two parts of the activity can be used as an extension where students are able to change the value of a in the quadratic function. They can also investigate the zeros of the graph when a, b, and c are not integers.