374 CHAPTER 3 Polynomial and Rational Functions Use a graphing calculator to find the coordinates of the turning points of the graph of each polynomial function in the given domain interval. Give answers to the nearest hundredth. 83. ƒ1x2 = 2x3 - 5x2 - x + 1; 3-1, 04 84. ƒ1x2 = x3 + 4x2 - 8x - 8; 30.3, 14 85. ƒ1x2 = 2x3 - 5x2 - x + 1; 31.4, 24 86. ƒ1x2 = x3 - x + 3; 3-1, 04 87. ƒ1x2 = x3 + 4x2 - 8x - 8; 3-3.8, -34 88. ƒ1x2 = x4 - 7x3 + 13x2 + 6x - 28; 3-1, 04 Solve each problem. 89. (Modeling) Social Security Numbers Your Social Security number (SSN) is unique, and with it you can construct your own personal Social Security polynomial. Let the polynomial function be defined as follows, where ai represents the ith digit in your SSN: SSN1x2 = 1x - a121x + a221x - a321x + a421x - a52 # 1x + a621x - a721x + a821x - a92. For example, for the SSN 539-58-0954, the polynomial function is SSN1x2 = 1x - 521x + 321x - 921x + 521x - 821x + 021x - 921x + 521x - 42. A comprehensive graph for this function is shown in Figure A. In Figure B, we show a screen obtained by zooming in on the positive zeros, as the comprehensive graph does not show the local behavior well in this region. Use a graphing calculator to graph your own “personal polynomial.” −1,000,000 −10 1,100,000 10 Figure A −129,268.3 3.18 152,439.02 9.77 Figure B 90. A comprehensive graph of ƒ1x2 = x4 - 7x3 + 18x2 - 22x + 12 is shown in the two screens, along with displays of the two real zeros. Find the two remaining nonreal complex zeros. −5 −1 10 4 −5 −1 10 4
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