To graph the function, start by putting the vertex on the axes. Then, choose a couple of values of x to the left or right of the vertex to plot more points. Use the axis of symmetry to fi nd the points (2, 2) and (3, 4) on the graph of f (x) 2(x 1)2 4. x y 0 2 1 4 x y 5 (3, 4) (1, 4) (1��2, 0) (1��2, 0) 5 5 (2, 2) (0, 2) f (x) 2(x 1)2 4 5 (1, 4) Axis of symmetry We can read the y-intercept from the graph: (0, 2). To fi nd the x-intercepts, let f (x) 0 and solve for x. f (x) 2(x 1)2 4 0 2(x 1)2 4 Substitute 0 for f (x). 4 2(x 1)2 Add 4. 2 (x 1)2 Divide by 2. 12 x 1 Square root property 1 12 x Add 1. The x-intercepts are (1 12, 0) and (1 12, 0). The domain is (q, q); the range is 4, q). YOU TRY 4 Graph f (x) 2(x 1)2 2. Also fi nd the x- and y-intercepts. When a quadratic function is written in the form f (x) ax2 bx c, there are two methods we can use to graph the function. Procedure Graphing Parabolas from the Form f(x) ax2 bx c There are two methods we can use to graph the function f (x) ax2 bx c. Method 1: Rewrite f (x) ax2 bx c in the form f (x) a(x h)2 k by completing the square. Method 2: Use the formula x b 2a to fi nd the x-coordinate of the vertex. Then, the vertex has coordinates a b 2a , f a b 2a bb. We will begin with Method 1. We will modify the steps we used in Section 10.1 to solve quadratic equations by completing the square. 658 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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