# Activities

• • • ##### Subject Area

• Math: Algebra I: Quadratic Functions

• ##### Author 9-12

90 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 3 from the EXPLORATIONS Book:
A Hands-On Look at Algebra Functions: Activities for Transformation Graphing .

## Exploring the Vertex Form of the Quadratic Function (Algebra Application)

#### Activity Overview

Students explore the vertex form of the parabola and discover how the vertex, direction, and width of the parabola can be determined by studying the parameters. They predict the location of the vertex of a parabola expressed in vertex form.

#### Before the Activity

• Set up the Transformation Graphing Application on the calculator using the TI Connect™ software
• See the attached PDF file for detailed instructions for this activity
• Print pages 20 - 26 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to your class.

• Graph a quadratic equation y = (x - 2)2 + 1 on the calculator and record its vertex and the direction in which the curve opens
• Use the Transformation Graphing application and enter the general vertex form of a quadratic equation Y = A(X - B)2 + C
• Identify the relationship between the values of A, B, and C (the coefficients) and the vertex and magnitude of the graph
• Value of B gives the x-coordinate of the vertex;
for the equation Y = (X - 3)2, B = 3 and the vertex is at X = 3;
for the equation Y = (X + 1)2, B = -1 and the vertex at X = -1
• Changes in C create a vertical translation of the curve; when C increases the curve moves up; when C decreases the curve moves down; Value of C is the y-coordinate of the vertex
• Value of A determines the direction of the parabola and its width; larger the magnitude of A, the narrower the curve; smaller the magnitude of A, the wider the curve; a positive sign means the parabola is opening up; a negative sign means the parabola is opening down
• Observe the direction in which the graph opens and determine the maximum/minimum values
• #### After the Activity

Students will complete the Student Worksheet and answer questions listed on it.

• Review student results
• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary