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c) To solve x2 2x 3 0 means to fi nd the x-values for which the y-values of the function y x2 2x 3 are greater than or equal to zero. (Recall that the x-intercepts are where the function equals zero.) The y-values of the function are greater than or equal to zero when x 1 or when x 3. The solution set of x2 2x 3 0 is (q, 1 ´ 3, q). y 5 x 1 y x y 5 5 5 When x 1 or x 3, the y-values are greater than or equal to 0. x YOU TRY 1 a) Graph y x2 6x 5. b) Solve x2 6x 5 0. c) Solve x2 6x 5 0. 2 Solve a Quadratic Inequality Using Test Points Example 1 illustrates how the x-intercepts of y x2 2x 3 break up the x-axis into the three separate intervals: x 1, 1 x 3, and x 3. We can use this idea of intervals to solve a quadratic inequality without graphing. EXAMPLE 2 Solve x2 2x 3 0. Solution Begin by solving the equation x2 2x 3 0. x2 2x 3 0 (x 3)(x 1) 0 Factor. x 3 0 or x 1 0 Set each factor equal to 0. x 3 or x 1 Solve. (These are the x-intercepts of y x2 2x 3.) Note The indicates that we want to find the values of x that will make x2 2x 3 0; that is, find the values of x that make x2 2x 3 a negative number. Put x 3 and x 1 on a number line with the smaller number on the left. This breaks up the number line into three intervals: x 1, 1 x 3, and x 3. Choose a test number in each interval and substitute it into x2 2x 3 to determine whether that value makes x2 2x 3 positive or negative. (If one number Be sure that you understand what is being done in each step. 682 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith


messersmith_power_intermediate_algebra_1e_ch4_7_10
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