Education Technology

Exploring Transformations of the Quadratic Function

Published on 02/19/2007

Activity Overview

Using TI-Interactive, students will discover how the variables of a, h, and k in the vertex form of a quadratic function affect the size, shape and location of the parabola. During the lesson students will write quadratic functions when given a graph and will graph the parabola given a quadratic function.

Before the Activity

In previous lessons students should learn about parabolas by graphing quadratic functions using a table of values. Vocabulary of vertex, maximum, minimum, y-intercept and axis of symmetry should be stressed. Students should also have learned to change a quadratic function in standard form (f(x)=ax^2+bx+c) to the vertex form (f(x)=a(x+h)^2+k) by completing the square.

During the Activity

Using the first page of the TI-Interactive document, students discover what affect changing the values of a, h, and k, has on a basic parabola. If only one program is available the discussion can be teacher led by projecting on a smart board or screen. It can also be done by individual students if enough programs and computers are available. After this discovery, use the rest of the TI-Interactive document to change a variable or variables to the correct value to move the dotted blue line to match the solid red line on each graph. Students can then write the correct vertex form of the function on their handout. Using the PowerPoint download and the empty grids on the handout, students are to sketch the parabola for the given quadratic functions.

After the Activity

Assign the worksheet to check students? understanding of the lesson.