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.

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.

Follow the activity procedures:

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