Turning_point

Turning_point - h 2.5 k -4.25 -1.75 -5 0 2.5 -4.25 (2.5,...

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Unformatted text preview: h 2.5 k -4.25 -1.75 -5 0 2.5 -4.25 (2.5, -4.25) 0 7 x -7 -6.9 -6.8 -6.7 -6.6 -6.5 -6.4 -6.3 -6.2 -6.1 -6 -5.9 -5.8 -5.7 -5.6 -5.5 -5.4 -5.3 -5.2 -5.1 -5 -4.9 -4.8 -4.7 -4.6 -4.5 -4.4 -4.3 y1 49 47.61 46.24 44.89 43.56 42.25 40.96 39.69 38.44 37.21 36 34.81 33.64 32.49 31.36 30.25 29.16 28.09 27.04 26.01 25 24.01 23.04 22.09 21.16 20.25 19.36 18.49 y2 90.25 88.36 86.49 84.64 82.81 81 79.21 77.44 75.69 73.96 72.25 70.56 68.89 67.24 65.61 64 62.41 60.84 59.29 57.76 56.25 54.76 53.29 51.84 50.41 49 47.61 46.24 y3 86 84.11 82.24 80.39 78.56 76.75 74.96 73.19 71.44 69.71 68 66.31 64.64 62.99 61.36 59.75 58.16 56.59 55.04 53.51 52 50.51 49.04 47.59 46.16 44.75 43.36 41.99 -4.2 -4.1 -4 -3.9 -3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3.2 -3.1 -3 -2.9 -2.8 -2.7 -2.6 -2.5 -2.4 -2.3 -2.2 -2.1 -2 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 17.64 16.81 16 15.21 14.44 13.69 12.96 12.25 11.56 10.89 10.24 9.61 9 8.41 7.84 7.29 6.76 6.25 5.76 5.29 4.84 4.41 4 3.61 3.24 2.89 2.56 2.25 1.96 1.69 1.44 1.21 1 0.81 0.64 0.49 0.36 0.25 0.16 0.09 0.04 0.01 0 0.01 0.04 0.09 0.16 0.25 0.36 0.49 0.64 0.81 1 44.89 43.56 42.25 40.96 39.69 38.44 37.21 36 34.81 33.64 32.49 31.36 30.25 29.16 28.09 27.04 26.01 25 24.01 23.04 22.09 21.16 20.25 19.36 18.49 17.64 16.81 16 15.21 14.44 13.69 12.96 12.25 11.56 10.89 10.24 9.61 9 8.41 7.84 7.29 6.76 6.25 5.76 5.29 4.84 4.41 4 3.61 3.24 2.89 2.56 2.25 40.64 39.31 38 36.71 35.44 34.19 32.96 31.75 30.56 29.39 28.24 27.11 26 24.91 23.84 22.79 21.76 20.75 19.76 18.79 17.84 16.91 16 15.11 14.24 13.39 12.56 11.75 10.96 10.19 9.44 8.71 8 7.31 6.64 5.99 5.36 4.75 4.16 3.59 3.04 2.51 2 1.51 1.04 0.59 0.16 -0.25 -0.64 -1.01 -1.36 -1.69 -2 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 1.21 1.44 1.69 1.96 2.25 2.56 2.89 3.24 3.61 4 4.41 4.84 5.29 5.76 6.25 6.76 7.29 7.84 8.41 9 9.61 10.24 10.89 11.56 12.25 12.96 13.69 14.44 15.21 16 16.81 17.64 18.49 19.36 20.25 21.16 22.09 23.04 24.01 25 26.01 27.04 28.09 29.16 30.25 31.36 32.49 33.64 34.81 36 37.21 38.44 39.69 1.96 1.69 1.44 1.21 1 0.81 0.64 0.49 0.36 0.25 0.16 0.09 0.04 0.01 0 0.01 0.04 0.09 0.16 0.25 0.36 0.49 0.64 0.81 1 1.21 1.44 1.69 1.96 2.25 2.56 2.89 3.24 3.61 4 4.41 4.84 5.29 5.76 6.25 6.76 7.29 7.84 8.41 9 9.61 10.24 10.89 11.56 12.25 12.96 13.69 14.44 -2.29 -2.56 -2.81 -3.04 -3.25 -3.44 -3.61 -3.76 -3.89 -4 -4.09 -4.16 -4.21 -4.24 -4.25 -4.24 -4.21 -4.16 -4.09 -4 -3.89 -3.76 -3.61 -3.44 -3.25 -3.04 -2.81 -2.56 -2.29 -2 -1.69 -1.36 -1.01 -0.64 -0.25 0.16 0.59 1.04 1.51 2 2.51 3.04 3.59 4.16 4.75 5.36 5.99 6.64 7.31 8 8.71 9.44 10.19 6.4 6.5 6.6 6.7 6.8 6.9 7 7.05 7.1 7.15 7.2 7.25 7.3 7.35 7.4 7.45 7.5 7.55 7.6 7.65 7.7 7.75 7.8 7.85 7.9 7.95 8 8.05 8.1 8.15 8.2 8.25 8.3 8.35 8.4 8.45 8.5 8.55 8.6 8.65 8.7 8.75 8.8 8.85 8.9 8.95 9 9.05 9.1 9.15 9.2 9.25 9.3 40.96 42.25 43.56 44.89 46.24 47.61 49 49.7 50.41 51.12 51.84 52.56 53.29 54.02 54.76 55.5 56.25 57 57.76 58.52 59.29 60.06 60.84 61.62 62.41 63.2 64 64.8 65.61 66.42 67.24 68.06 68.89 69.72 70.56 71.4 72.25 73.1 73.96 74.82 75.69 76.56 77.44 78.32 79.21 80.1 81 81.9 82.81 83.72 84.64 85.56 86.49 15.21 16 16.81 17.64 18.49 19.36 20.25 20.7 21.16 21.62 22.09 22.56 23.04 23.52 24.01 24.5 25 25.5 26.01 26.52 27.04 27.56 28.09 28.62 29.16 29.7 30.25 30.8 31.36 31.92 32.49 33.06 33.64 34.22 34.81 35.4 36 36.6 37.21 37.82 38.44 39.06 39.69 40.32 40.96 41.6 42.25 42.9 43.56 44.22 44.89 45.56 46.24 10.96 11.75 12.56 13.39 14.24 15.11 16 16.45 16.91 17.37 17.84 18.31 18.79 19.27 19.76 20.25 20.75 21.25 21.76 22.27 22.79 23.31 23.84 24.37 24.91 25.45 26 26.55 27.11 27.67 28.24 28.81 29.39 29.97 30.56 31.15 31.75 32.35 32.96 33.57 34.19 34.81 35.44 36.07 36.71 37.35 38 38.65 39.31 39.97 40.64 41.31 41.99 9.35 9.4 9.45 9.5 9.55 9.6 9.65 9.7 9.75 9.8 9.85 9.9 9.95 10 10.05 10.1 10.15 10.2 10.25 10.3 10.35 10.4 10.45 10.5 10.55 10.6 10.65 10.7 10.75 10.8 10.85 10.9 10.95 11 11.05 11.1 11.15 11.2 11.25 11.3 11.35 11.4 11.45 11.5 11.55 11.6 11.65 11.7 11.75 11.8 11.85 11.9 11.95 87.42 88.36 89.3 90.25 91.2 92.16 93.12 94.09 95.06 96.04 97.02 98.01 99 100 101 102.01 103.02 104.04 105.06 106.09 107.12 108.16 109.2 110.25 111.3 112.36 113.42 114.49 115.56 116.64 117.72 118.81 119.9 121 122.1 123.21 124.32 125.44 126.56 127.69 128.82 129.96 131.1 132.25 133.4 134.56 135.72 136.89 138.06 139.24 140.42 141.61 142.8 46.92 47.61 48.3 49 49.7 50.41 51.12 51.84 52.56 53.29 54.02 54.76 55.5 56.25 57 57.76 58.52 59.29 60.06 60.84 61.62 62.41 63.2 64 64.8 65.61 66.42 67.24 68.06 68.89 69.72 70.56 71.4 72.25 73.1 73.96 74.82 75.69 76.56 77.44 78.32 79.21 80.1 81 81.9 82.81 83.72 84.64 85.56 86.49 87.42 88.36 89.3 42.67 43.36 44.05 44.75 45.45 46.16 46.87 47.59 48.31 49.04 49.77 50.51 51.25 52 52.75 53.51 54.27 55.04 55.81 56.59 57.37 58.16 58.95 59.75 60.55 61.36 62.17 62.99 63.81 64.64 65.47 66.31 67.15 68 68.85 69.71 70.57 71.44 72.31 73.19 74.07 74.96 75.85 76.75 77.65 78.56 79.47 80.39 81.31 82.24 83.17 84.11 85.05 12 12.05 12.1 12.15 12.2 12.25 12.3 12.35 12.4 12.45 12.5 12.55 12.6 12.65 12.7 12.75 12.8 12.85 12.9 12.95 13 13.05 13.1 13.15 13.2 13.25 13.3 13.35 13.4 13.45 13.5 13.55 13.6 13.65 13.7 13.75 13.8 13.85 13.9 13.95 14 14.05 14.1 14.15 14.2 14.25 14.3 14.35 14.4 14.45 14.5 14.55 14.6 144 145.2 146.41 147.62 148.84 150.06 151.29 152.52 153.76 155 156.25 157.5 158.76 160.02 161.29 162.56 163.84 165.12 166.41 167.7 169 170.3 171.61 172.92 174.24 175.56 176.89 178.22 179.56 180.9 182.25 183.6 184.96 186.32 187.69 189.06 190.44 191.82 193.21 194.6 196 197.4 198.81 200.22 201.64 203.06 204.49 205.92 207.36 208.8 210.25 211.7 213.16 90.25 91.2 92.16 93.12 94.09 95.06 96.04 97.02 98.01 99 100 101 102.01 103.02 104.04 105.06 106.09 107.12 108.16 109.2 110.25 111.3 112.36 113.42 114.49 115.56 116.64 117.72 118.81 119.9 121 122.1 123.21 124.32 125.44 126.56 127.69 128.82 129.96 131.1 132.25 133.4 134.56 135.72 136.89 138.06 139.24 140.42 141.61 142.8 144 145.2 146.41 86 86.95 87.91 88.87 89.84 90.81 91.79 92.77 93.76 94.75 95.75 96.75 97.76 98.77 99.79 100.81 101.84 102.87 103.91 104.95 106 107.05 108.11 109.17 110.24 111.31 112.39 113.47 114.56 115.65 116.75 117.85 118.96 120.07 121.19 122.31 123.44 124.57 125.71 126.85 128 129.15 130.31 131.47 132.64 133.81 134.99 136.17 137.36 138.55 139.75 140.95 142.16 14.65 14.7 14.75 214.62 216.09 217.56 147.62 148.84 150.06 143.37 144.59 145.81 Turning point form y = x2 + bx + d b -5 d 2 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 6 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### y 4 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 2 ### ### ### ### ### ### ### ### ### ### ### ### y = x2 - 5x + 2 Graphs of y = x and y = (x shown 2 ) − 2.5 are also 2 0 ### ### ### ### ### ### ### ### ### ### ### x ### ### ### ### ### ### ### ### ### ### ### ### ### -2 ### ### ### ### ### ### ### ### ### ### ### ### Turning point form: y = (x − 2.5 )2 − 4.25 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### -4 ### ### ### ### ### ### ### ### ### ### ### ### -6 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### + Coordinates of turning point: (2.5, -4.25) EXIT EXCEL -8 ### ### ### ### ### ### ### ### ### ### ### ### -10 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### -12 ### -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -10 -12 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### 44444 ### ### ### ### ### ### ### ### ### ### ### 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This note was uploaded on 04/12/2011 for the course MATH 2180 taught by Professor Staff during the Spring '11 term at North Texas.

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