Learning Resources

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Outcomes

In this lesson you will learn

  • to solve a quadratic inequality by using the graph
  • to solve a quadratic inequality by using a sign graph (number line)
  • the effect of multiplying an inequality by a negative number
  • the use of interval notation

By the end of this section students will be able to:

  • analyze relations, functions and their graphs
  • use tables and graphs as tools to interpret expressions
  • analyze and solve polynomial, rational, irrational, absolute value and trigonometric equations
  • analyze and solve polynomial, rational, irrational and absolute inequalities
  • model real-world phenomena with a variety of functions/relations
  • determine the equations of polynomial and rational functions
  • factor polynomial equations

Introduction

Now that you have practiced sketching the graphs of quadratic, cubic and quartic functions, you should realize the importance of knowing the roots of these equations. In Focus B, however, you probably noticed that the cubic and quartic functions were always stated in factored form to enable you to readily identify the x-intercepts. If the polynomial equation is not stated in factored form, then methods to solve these equations must be available.

These solution methods will then be extended to include finding the solution to inequalities. For example, you already have the skills needed to solve the equation x2 + 7x + 10 = 0. How then, can you use these skills to solve the inequalities x2 + 7x + 10 > 0 and  x2  + 7x + 10 < 0? You may have some thoughts on this process already. Nonetheless, you will learn methods for solving these as well as cubic and quartic inequalities.

Again, graph paper is needed for many of the activities. Be sure to have some with you for each lesson.

This section of study should take 4 to 5 hours to complete.

Prerequisites

To be successful in this lesson, it would be helpful to know the following:

  • how to find the zeros of a quadratic function from examining its graph
  • how to graphically illustrate solution sets on a number line