c) x y 5 5 5 5 d) x y 5 5 5 5 Exercises 41–46 each present a shift that is performed on the graph of f (x) x2 to obtain the graph of g(x). Write the equation of g(x). 41) f(x) is shifted 8 units to the right. 42) f(x) is shifted down 9 units. 43) f(x) is shifted up 3.5 units. 44) f(x) is shifted left 1.2 units. 45) f(x) is shifted left 4 units and down 7 units. 46) f(x) is shifted up 2 units and right 5 units. Objective 3: Graph f(x) ax2 bx c by Completing the Square Rewrite each function in the form f (x) a(x h)2 k. 48) f (x) x2 4x 7 f (x) (x2 4x) 7 f (x) (x 2)2 11 Find the number that completes the square in the parentheses. Add and subtract the number above to the same side of the equation. Rewrite each function in the form f (x) a(x h)2 k by completing the square. Then, graph the function. Include the intercepts. Determine the domain and range. 49) f (x) x2 2x 3 50) g(x) x2 6x 8 51) y x2 6x 7 52) h(x) x2 4x 1 53) g(x) x2 4x 54) y x2 8x 18 55) h(x) x2 4x 5 56) f (x) x2 2x 3 57) y x2 6x 10 58) g(x) x2 4x 6 59) y 2x2 8x 2 60) f (x) 2x2 8x 4 61) g(x) 1 3 x2 2x 9 62) h(x) 1 2 x2 3x 19 2 63) y x2 3x 2 64) f (x) x2 5x 21 4 Objective 4: Graph f(x) ax2 bx c Using a b 2a , f a b 2a bb Graph each function using the vertex formula. Include the intercepts. Determine the domain and range. 65) y x2 2x 3 66) g(x) x2 6x 8 67) f (x) x2 8x 13 68) y x2 2x 2 69) g(x) 2x2 4x 4 70) f (x) 4x2 8x 6 71) y 3x2 6x 1 72) h(x) 2x2 12x 9 73) f (x) 1 2 x2 4x 5 74) y 1 2 x2 2x 3 75) h(x) 1 3 x2 2x 5 76) g(x) 1 5 x2 2x 8 Fill It In Fill in the blanks with either the missing mathematical step or the reason for the given step. 47) f (x) x2 8x 11 Group the variable terms together using parentheses. Find the number that completes the square in the parentheses. f (x) (x2 8x 16) 11 16 Factor and simplify. 666 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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