Definition/Procedure Example Graphing Basic Parabolas The simplest form of a quadratic equation is y x2. (p. 631) The lowest point on a parabola that opens upward or the highest point on a parabola that opens downward is called the vertex. (p. 631) Graphing a Parabola of the Form y ax2 bx c (a 0) Step 1: Find the vertex. The x-coordinate of the vertex is (2, 4) 5 5 y x2 (2, 4) CHAPTER 10 Summary 655 x b 2a . Find the y-coordinate of the vertex by substituting the x-value in 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. (p. 634) Graph y x2 4x 3. Step 1: Find the vertex. x b 2a 4 2(1) 2 y (2)2 4(2) 3 4 8 3 1 The vertex of the parabola is (2, 1). Step 2: Find the y-intercept: y (0)2 4(0) 3 3 The y-intercept is (0, 3). Step 3: Find the x-intercepts: 0 x2 4x 3 0 (x 3)(x 1) x 3 or x 1 The x-intercepts are (3, 0) and (1, 0). Step 4: Find an additional point: Let x 4. y (4)2 4(4) 3 16 16 3 3 Another point on the graph is (4, 3). x y 5 5 5 y x2 4x 3 Vertex (2, 1) Graph y x2. x y 5 5 5 (0, 0) (1, 1) (1, 1) Vertex The graph of a quadratic equation of the form y ax2 bx c is called a parabola. (p. 631) The graph of y 2x2 x 9 is a parabola. 10.4 Graphs of Quadratic Equations x y 0 0 1 1 2 4 1 1 2 4 www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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