Education Technology

The Standard Form of a Quadratic equation

Published on 06/09/2008

Activity Overview

In this activity, students explore the standard form of a quadratic equation, y = ax 2 + bx + c. They explore how the x-intercepts (zeros), y-intercept, and vertex are related to the graph of the standard form of a quadratic function.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 49 - 53 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Define and graph a quadratic equation
  • Determine the values of the x-intercepts
  • Observe that these are the points where the graph crosses the x-axis
  • Determine the value of the y-intercept
  • Observe that this is the point where the graph crosses the y-axis
  • Determine the coordinates of the vertex, the point with the lowest value of y
  • Find the value of y for x = -4, -1, 0, and 2
  • Find the zeros and factors of the expression
  • Find the zeros of the factors
  • Observe that the zeros of each factor and zeros of the function are the same, and also the zeros of the function and the x-intercept are the same
  • Observe that the x-intercepts can be found without graphing, by first finding the factors, and then finding their zeros
  • Observe that the value of y when x = 0 and the y-intercept are the same
  • After the Activity

    Students complete the Student Activity sheet.

    Review student results:

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