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21) The Soo family wants to fence in a rectangular area to hold their dogs. One side of the pen will be their barn. Find the dimensions of the pen of greatest area that can be enclosed with 48 ft of fencing. 22) A farmer wants to enclose a rectangular area with 120 ft of fencing. One side is a river and will not require a fence. What is the maximum area that can be enclosed? 23) Find two integers whose sum is 18 and whose product is a maximum. 24) Find two integers whose sum is 26 and whose product is a maximum. 25) Find two integers whose difference is 12 and whose product is a minimum. 26) Find two integers whose difference is 30 and whose product is a minimum. Objective 4: Graph Parabolas of the Form x a(y k)2 h Given a quadratic equation of the form x a(y k)2 h, answer the following. 27) What is the vertex? 28) What is the equation of the axis of symmetry? 29) If a is negative, which way does the parabola open? 30) If a is positive, which way does the parabola open? For each equation, identify the vertex, axis of symmetry, and x- and y-intercepts. Then, graph the equation. Determine the domain and range. 31) x (y 1)2 4 32) x (y 3)2 1 33) x y2 2 34) x (y 4)2 35) x (y 4)2 5 36) x (y 1)2 7 37) x 2(y 2)2 9 38) x 1 2 (y 4)2 7 39) x 1 4 ( y 2)2 40) x 2y2 3 Objective 5: Rewrite x ay2 by c as x a(y k)2 h by Completing the Square Rewrite each equation in the form x a(y k)2 h by completing the square and graph it. Determine the domain and range. 41) x y2 4y 6 42) x y2 4y 5 43) x y2 2y 5 44) x y2 6y 6 45) x 1 3 y2 8 3 y 5 3 46) x 2y2 4y 5 47) x 4y2 8y 10 48) x 1 2 y2 4y 1 Objective 6: Find the Vertex of x ay2 by c Using y b 2a , and Graph the Equation Graph each equation using the vertex formula. Find the x- and y-intercepts. Determine the domain and range. 49) x y2 4y 3 50) x y2 2y 2 51) x y2 4y 52) x y2 6y 4 53) x 2y2 4y 6 54) x 3y2 6y 1 55) x 4y2 16y 13 56) x 2y2 4y 8 57) x 1 4 y2 1 2 y 25 4 58) x 3 4 y2 3 2 y 11 4 Mixed Exercises Exercises 59–68 contain parabolas that open either horizontally or vertically. Graph each equation. Determine the domain and range. 59) h(x) x2 6 60) y x2 6x 1 61) x y2 62) f (x) 3x2 12x 8 63) x 1 2 y2 4y 5 64) x (y 4)2 3 65) y x2 2x 3 66) x 3(y 2)2 11 67) f (x) 2(x 4)2 3 68) g(x) 3 2 x212x20 R1) What does it mean to have a maximum or a minimum? R2) How does a parabola open left or right? R3) What do you fi nd most diffi cult about solving applied problems? Which type is the hardest for you? SECTION 10.6 Applications of Qu www.mhhe.com/messersmith adratic Functions and Graphing Other Parabolas 679


messersmith_power_intermediate_algebra_1e_ch4_7_10
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