Solving Graphic Equations with the Zero Method: Finding Quadratic Equation Roots

Prior Knowledge

In this lesson, students will be taught how to find solutions to quadratic equations using the zero method, or the zero finder, on their T1-83 graphing calculator. This lesson assumes students are already familiar with solving simple quadratic equations by hand, and that they have become relatively comfortable using their graphing calculator for solving arithmetic problems and simple algebra problems.

Student Objectives

In this lesson, students will:

  • Learn the following vocabulary words: intersection finder, zero finder, roots, root finder, 2nd degree polynomials, 3rd degree polynomials, parabola, y-intercept, x-intercept
  • Learn which buttons on their graphing calculator will enable them to solve a quadratic equation by finding the roots (e.g., the x-intercepts)
  • Listen to the teacher's lecture on using the zero method to solve graphic equations
  • Solve sample exercises the teacher provides during the class session to test their comprehension of the material

Learning Activities Breakdown

1) Provide an overview of the day's lesson, and ensure students to take out their calculator, a pencil, and sheet of scratch paper if needed.

2) Begin the lecture by explaining finding the roots of a quadratic equation. Review how the roots (e.g., the values of x in the equation that will result in y = 0) of a quadratic equation can be solved algebraically, using a simple equation as an example: x2– x – 30.

3) Discuss how quadratic equations that are considerably more difficult to solve algebraically but can be solved relatively easily (e.g., find the zeroes) with the graphing calculator with the following example equation: 2x2 + 13x + 8.

4) Lead students in entering the equation in their calculator and finding the roots through the following steps:

  • Turn on the calculator; press the [Y=] button.
  • Type in the equation in the first available line (Y1=).
  • Press the [WINDOW] button and enter the following values: Xmin=-10, Xmax=10, Xsc=1, Ymin=-35, Ymax=35, Ysc=1, Xres=1.
  • Press the [GRAPH] button.
  • Press the [2nd] then [CALC] buttons.
  • Press 2 for "zero".
  • Press the left arrow until the cursor is to the left of one of the points where the parabola intersects with the x-axis, then press [ENTER].
  • Press the right arrow until the cursor is to the right of the same point where the parabola intersects with the x-axis, then press [ENTER].
  • Press [ENTER] again to have the calculator guess where the parabola intersects with the x-axis.

5) Provide students with several additional examples of increasing difficulty (2nd and 3rd degree polynomials), to try during the discussion. Have students provide their answers orally.

This post is part of the series: Learning About Graphs

This series of lesson plans outline ways to teach students topics pertaining to solving algebraic equations using graphs and graphing calculators.
  1. A Lesson on Graphing Equations Using the Graphing Calculator
  2. Teaching About the Rectangular Coordinate System
  3. Teaching the Zero Method For Solving Graphic Equations
  4. Lesson plan: Solving Graphic Equations with the Intersection Method
  5. Lesson Plan for Teaching Students to Solve Polynomial Equations