Section 1.3 Solving Equations Using a Graphing Utility Copyright © 2013 Pearson Education, Inc. All rights reserved

Equations in One Variable An equation in one variable is a statement in which two expressions, at least one containing the variable, are equal. The expressions are called the sides of the equation. The admissible values of the variable, if any, that result in a true statement are called solution, or roots, of the equation. To solve an equation means to find all the solutions of the equation. Copyright © 2013 Pearson Education, Inc. All rights reserved

Equations in One Variable Examples of an equation in one variable: x + 5 = 9 is true when x = 4. 4 is a solution of the equation or we say that 4 satisfies the equation. We write the solution in set notation, this is called the solution set of the equation. An equation that is satisfied for every choice of the variable for which both sides are defined is called an identity. Copyright © 2013 Pearson Education, Inc. All rights reserved

Solve Equations Using a Graphing Utility Copyright © 2013 Pearson Education, Inc. All rights reserved

There appears to be one x-intercept (solution) between –2 and –1. Using ZERO (or ROOT) to Approximate Solutions of an Equation Find the solution(s) of the equation x3 – x + 1 = 0. Round answers to two decimal places. The solutions of the equation x3 – x + 1 = 0 are the same as the x-intercepts of the graph of Y1 = x3 – x + 1. There appears to be one x-intercept (solution) between –2 and –1. Copyright © 2013 Pearson Education, Inc. All rights reserved

Using ZERO (or ROOT) to Approximate Solutions of an Equation Using the ZERO (or ROOT) feature of a graphing utility, we determine that the x-intercept, and thus the solution to the equation, is x = –1.32 rounded to two decimal places. Copyright © 2013 Pearson Education, Inc. All rights reserved

Begin by graphing each side of the equation: Using INTERSECT to Approximate Solutions of an Equation Find the solution(s) to the equation 4x4 – 3 = 2x + 1. Round answers to two decimal places. Begin by graphing each side of the equation: Y1 = 4x4 – 3 and Y2 = 2x + 1. Copyright © 2013 Pearson Education, Inc. All rights reserved

Using INTERSECT to Approximate Solutions of an Equation At a point of intersection of the graphs, the value of the y-coordinate is the same for Y1 and Y2. Thus, the x-coordinate of the point of intersection represents a solution to the equation. Copyright © 2013 Pearson Education, Inc. All rights reserved

Using INTERSECT to Approximate Solutions of an Equation The INTERSECT feature on a graphing utility determines a point of intersection of the graphs. Using this feature, we find that the graphs intersect at (–0.87, –0.73) and (1.12, 3.23) rounded to two decimal places. Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved