EXAMPLE 1 In-Class Example 1 Use Example 1. Graph y x2. Solution Make a table of values. Plot the points, and connect them with a smooth curve. y x2 x y 0 0 1 1 2 4 1 1 2 4 x y 5 y x2 (2, 4) (1, 1) (0, 0) (2, 4) (1, 1) Vertex 5 5 5 The graphs of quadratic equations where y is defi ned in terms of x open either upward or downward. Notice that this graph opens upward. The lowest point on a parabola that opens upward or the highest point on a parabola that opens downward is called the vertex. The vertex of the graph of y x2 is (0, 0). When graphing a quadratic equation by plotting points, it is important to locate the vertex. YOU TRY 1 Graph y x2 3. EXAMPLE 2 Graph y (x 2)2. Solution In Example 1, we said that it is important to locate the vertex of a parabola. Let’s do that fi rst. Begin by fi nding the x-coordinate of the vertex of this graph. The x-coordinate of the vertex is the value of x that makes the expression being squared equal to zero. The x-coordinate of the vertex of this parabola is 2. Make a table of values, and use the x-coordinate of the vertex as the fi rst x-value in the table. Then, we will choose a couple of values of x that are larger than 2 and a couple of values that are smaller than 2. Find the corresponding y-values, plot the points, and connect them with a smooth curve. y (x 2)2 x y 2 0 3 1 4 4 1 1 0 4 x y 5 y (x 2)2 Vertex (1, 1) (2, 0) 5 5 (3, 1) (0, 4) (4, 4) 5 The vertex of this parabola is (2, 0). Notice that this time it is the highest point on the parabola because the graph opens downward. In-Class Example 2 Graph y (x 4)2. Answer: x 3 y y (x 4)2 Vertex (3, 1) (4, 0) 3 7 (2, 4) (6, 4) 7 (5, 1) YOU TRY 2 Graph y (x 3)2. 632 CHAPTER 10 Quadratic Equations www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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