When graphing a parabola, the fi rst point we should locate is the vertex. Procedure Graphing a Parabola of the Form y ax2 bx c Step 1: Find the vertex. The x-coordinate of the vertex is b 2a . Find the y-coordinate of the vertex by substituting the x-value into the equation. Step 2: Find the y-intercept by substituting 0 for x and solving for y. Step 3: Find the x-intercepts, if they exist, by substituting 0 for y and solving for x. Step 4: Find additional points on the parabola using a table of values. Step 5: Plot the points, and sketch the graph. Is there any more detail you would like to add to this procedure? EXAMPLE 3 In-Class Example 3 Graph y x2 2x 3. Answer: Graph y x2 4x 3. Solution Step 1: Find the vertex. First, fi nd the x-coordinate of the vertex: x b 2a 4 2(1) 4 2 2 a 1 b 4 Vertex (1, 4) y x2 2x 3 Next, substitute x 2 into the equation to fi nd the y-coordinate of the vertex. y x2 4x 3 y (2)2 4(2) 3 Substitute 2 for x. y 4 8 3 1 The vertex of the parabola is (2, 1). Step 2: Find the y-intercept by substituting 0 for x and solving for y: y x2 4x 3 y (0)2 4(0) 3 3 The y-intercept is (0, 3). Step 3: Find the x-intercepts by substituting 0 for y and solving for x: 0 x2 4x 3 Substitute 0 for y. 0 x2 4x 3 Divide both sides by 1. 0 (x 1)(x 3) Factor. b R x 1 or x 3 Solve. The x-intercepts are (1, 0) and (3, 0). x 5 y 5 5 5 634 CHAPTER 10 Quadratic Equations www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
To see the actual publication please follow the link above