Education Technology

Investigating the Parabola in Vertex Form (y = ax2 + bx + c)

Published on 06/09/2008

Activity Overview

In this activity, students investigate the standard form of the quadratic function, y = ax2 + bx + c. They investigate the changes on the graph of a quadratic equation that result from changes in A, B, and C. They also locate the vertex of a parabola when its quadratic equation is expressed in standard form.

Before the Activity

Install the Transformation Graphing application on the students' graphing calculators using one of these two methods:

  • TI-Connect™,  a TI Connectivity Cable, and the Unit-to-Unit Link Cable
  • TI-Navigator™  "send to class" feature
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 59 - 68 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Given the vertex form of a quadratic function, determine the coordinates of the vertex
  • Use the standard form of the quadratic equation
  • Change the value of C and examine the effect on the graph
  • Understand that the value of C gives the y-intercept of a parabola
  • Keeping A constant, observe how the graph changes as value of B changes
  • Notice the relationship between the x-coordinate and the value of B
  • Change the value of A and notice what happens to the x-coordinate and the graph of the parabola
  • Write an expression relating the values of A and B to the x-coordinate of the vertex
  • Observe that given the vertex, y-intercept and a symmetric point, a parabola can be graphed
  • After the Activity

    Students will complete the Student Worksheet and answer questions.

    Review student results:

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