30 CHAPTER 1 Graphs A second method for solving equations using a graphing utility involves the INTERSECT feature of the graphing utility. This feature is used most effectively when neither side of the equation is 0. Figure 45 Solution Begin by graphing each side of the equation as follows: graph = − Y x4 3 1 4 and = + Y x2 1. 2 See Figure 44(a). At a point of intersection of the graphs, the value of the y-coordinate is the same for Y1 and Y .2 Thus, the x-coordinate of the point of intersection represents a solution to the equation. Do you see why? The INTERSECT feature on a graphing utility determines a point of intersection of the graphs. Using this feature, find that the graphs intersect at ( ) − − 0.87, 0.73 and ( ) 1.12, 3.23 rounded to two decimal places. See Figures 44(b) and (c). The solutions of the equation are −0.87 and 1.12 rounded to two decimal places. Using INTERSECT to Approximate Solutions of an Equation Find the solution(s) of the equation − = + x x 4 3 2 1. 4 Round answers to two decimal places. EXAMPLE 2 (c) 10 210 24 4 (b) 10 210 24 4 (a) = − Y x4 3; 1 4 = + Y x2 1 2 10 Y1 Y2 210 24 4 Figure 44 Now Work PROBLEM 7 If you are using Geogebra or Desmos, graph each side of the equation as we did in Example 2. Then, click on one of the graphs to identify the points of intersection. See Figure 45 where Desmos is used to determine the solutions of the equation as −0.87 and 1.12 rounded to two decimal places.
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