20 CHAPTER 1 Graphs 1.3 Intercepts; Symmetry; Graphing Key Equations Now Work the ‘Are You Prepared?’ problems on page 26. • Solving Linear Equations (Section A.6, pp. A45–A47) • Solving Quadratic Equations (Section A.6, pp. A47–A53) PREPARING FOR THIS SECTION Before getting started, review the following: Figure 30 y 5 (4, 0) x 5 ( 1, 0) 4, 0) 25 5 (0, 23) 2 (2 2 Procedure for Finding Intercepts • To find the x -intercept(s), if any, of the graph of an equation, let = y 0 in the equation and solve for x, where x is a real number. • To find the y -intercept(s), if any, of the graph of an equation, let = x 0 in the equation and solve for y, where y is a real number. OBJECTIVES 1 Find Intercepts Algebraically from an Equation (p. 20) 2 Test an Equation for Symmetry with Respect to the x -Axis, the y -Axis, and the Origin (p. 21) 3 Know How to Graph Key Equations (p. 24) 1 Find Intercepts Algebraically from an Equation In Section 1.1,we discussed how to find intercepts from a graph and how to approximate intercepts from an equation using a graphing utility. Now we discuss how to find intercepts from an equation algebraically. To better understand the procedure, look at Figure 30. From the graph, note that the intercepts are ( ) ( ) ( ) − − 4,0 , 1,0 , 4,0 , and ( ) − 0, 3 . The x -intercepts are − − 4, 1, and 4. The y -intercept is −3. Notice that x -intercepts have y -coordinates that equal 0; y -intercepts have x -coordinates that equal 0. This leads to the following procedure for finding intercepts. Finding Intercepts from an Equation Find the x -intercept(s) and the y -intercept(s) of the graph of = − y x 4. 2 Then graph = − y x 4 2 by plotting points. Solution To find the x -intercept(s), let = y 0 and obtain the equation ( )( ) − = + − = + = − = = − = x x x x x x x 4 0 2 2 0 2 0 or 2 0 2 or 2 2 The equation has two solutions, −2 and 2. The x -intercepts are −2 and 2. To find the y -intercept(s), let = x 0 in the equation. = − = − = − y x 4 0 4 4 2 2 The y -intercept is −4. y x y 4 with 0 2 = − = Factor. Use the Zero-Product Property. Solve. EXAMPLE 1
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