For each quadratic function, identify the vertex, axis of symmetry, and x- and y-intercepts. Then, graph the function. Determine the domain and range. 73) f (x) x2 4 74) h(x) (x 1)2 75) f (x) (x 2)2 1 76) y 2x2 77) y (x 4)2 2 78) g(x) 1 2 (x 3)2 2 79) If the graph of f (x) x2 is shifted 6 units to the right to obtain the graph of g(x), what is the equation of g(x)? 80) What are two ways to fi nd the vertex of the graph of f (x) ax2 bx c? 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. 81) f (x) x2 2x 3 82) y x2 4x 1 83) y 1 2 x2 4x 9 84) f (x) 2x2 8x 2 Graph each equation using the vertex formula. Include the intercepts. Determine the domain and range. 85) y x2 6x 10 86) f (x) x2 2x 4 (10.6) Solve. 87) An object is thrown upward from a height of 240 ft so that its height h (in feet) t sec after being thrown is given by h(t) 16t2 32t 240. a) How long does it take the object to reach its maximum height? b) What is the maximum height attained by the object? c) How long does it take the object to hit the ground? 88) A restaurant wants to add outdoor seating to its inside service. It has 56 ft of fencing to enclose a rectangular, outdoor café. Find the dimensions of the outdoor café of maximum area if the building will serve as one side of the café. For each quadratic equation, identify the vertex, axis of symmetry, and x- and y-intercepts. Then, graph the equation. Determine the domain and range. 89) x (y 3)2 11 90) x (y 1)2 5 Rewrite each equation in the form x a(y k)2 h by completing the square. Then, graph the equation. Include the intercepts. Determine the domain and range. 91) x y2 8y 7 92) x y2 4y 4 Graph each equation using the vertex formula. Include the intercepts. Determine the domain and range. 93) x 1 2 y2 3y 5 2 94) x 3y2 12y Write an equation, and solve. 67) Ayesha is making a pillow sham by sewing a border onto an old pillow case. The rectangular pillow case measures 18 in. by 27 in. When she sews a border of uniform width around the pillowcase, the total area of the surface of the pillow sham will be 792 in2. How wide is the border? 68) The width of a rectangular piece of cardboard is 4 in. less than its length. A square piece that measures 2 in. on each side is cut from each corner, then the sides are turned up to make a box with volume 280 in3. Find the length and width of the original piece of cardboard. 69) A fl ower shop determined that the demand, D(P), for its tulip bouquet is D(P) 240 P per week, where P is the price of the bouquet in dollars. The weekly supply, S(P), is given by S(P) 4p 2. Find the price at which demand for the tulips equals the supply. 70) U.S. sales of a certain brand of wine can be modeled by y 0.20x2 4.0x 8.4 for the years 1995–2010. x is the number of years after 1995, and y is the number of bottles sold, in millions. a) How many bottles were sold in 1995? b) How many bottles were sold in 2008? c) In what year did sales reach 28.4 million bottles? (10.5) 71) Given a quadratic function in 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) what does the sign of a tell us about the graph of f ? 72) Match each function to its graph. f (x) (x 2)2, g(x) x2 2, h(x) x2 2, k(x) (x 2)2 x y 5 5 5 5 x y 5 5 5 5 x y 5 5 5 5 x y 5 5 5 5 698 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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