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b) x y 5 5 5 5 c) x y 5 4 6 5 d) x y 5 5 5 5 40) f (x) (x 1)2, g(x) x2 1, h(x) (x 1)2, k(x) x2 1 a) x y 5 5 5 5 b) x y 5 5 5 5 Objective 2: Graph f (x) a(x h)2 k Using Characteristics of a Parabola 19) Given a quadratic function of the form f (x) a(x h)2 k, a) what is the vertex? b) what is the equation of the axis of symmetry? c) how do you know if the parabola opens upward? d) how do you know if the parabola opens downward? e) how do you know if the parabola is narrower than the graph of y x2? f) how do you know if the parabola is wider than the graph of y x2? For each quadratic function, identify the vertex, axis of symmetry, and x- and y-intercepts. Then, graph the function. Determine the domain and range. 20) g(x) (x 3)2 1 21) f (x) (x 1)2 4 22) h(x) (x 2)2 7 23) g(x) (x 2)2 3 24) y (x 1)2 5 25) y (x 4)2 2 26) g(x)(x3)22 27) f (x) (x 3)2 6 28) f (x)(x2)24 29) y (x 1)2 5 30) y 2(x 1)2 2 31) f (x) 2(x 1)2 8 32) h(x) 1 2 (x 4)2 33) g(x) 1 4 x2 1 34) y x2 5 35) f (x) 1 3 (x 4)2 3 36) y 1 2 (x 4)2 2 37) g(x) 3(x 2)2 5 38) f (x) 2(x 3)2 3 In Exercises 39 and 40, match each function to its graph. 39) f (x) x2 3, g(x) (x 3)2, h(x) (x 3)2, k(x) x2 3 a) x y 5 6 4 5 www.mhhe.com/messersmith SECTION 10.5 Quadratic Functions and Their Graphs 665


messersmith_power_intermediate_algebra_1e_ch4_7_10
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