Graph each equation. Find the x- and y-intercepts and the domain and range. a) x (y 2)2 1 b) x 2(y 2)2 4 Solution a) 1) h 1 and k 2. The vertex is (1, 2). 2) The axis of symmetry is y 2. 3) a 1, so the parabola opens to the right. It is the same width as y x2. To fi nd the x-intercept, let y 0 and solve for x. x ( y 2)2 1 x (0 2)2 1 x 4 1 3 The x-intercept is (3, 0). y 5 5 1 5 5 V 1 2 Find the y-intercepts by substituting 0 for x and solving for y. x ( y 2)2 1 0 ( y 2)2 1 Substitute 0 for x. 1 ( y 2)2 Add 1. 1 y 2 Square root property b R 1 y 2 or 1 y 2 1 y 3 y Solve. The y-intercepts are (0, 3) and (0, 1). Use the axis of symmetry to locate the point (3, 4) on the graph. The domain is 1, q), and the range is (q, q). b) x 2(y 2)2 4 1) h 4 and k 2. The vertex is (4, 2). 2) The axis of symmetry is y 2. 3) a 2, so the parabola opens to the left. It is narrower than y x2. To fi nd the x-intercept, let y 0 and solve for x. x 2(y 2)2 4 x 2(0 2)2 4 x 2(4) 4 4 The x-intercept is (4, 0). EXAMPLE 4 x x y 5 5 5 V 2 5 Do you notice the similarities and differences between graphing these equations and graphing quadratic functions? SECTION 10.6 Applications of Qu www.mhhe.com/messersmith adratic Functions and Graphing Other Parabolas 673
messersmith_power_intermediate_algebra_1e_ch4_7_10
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