Quadratics and inequalities

92 sharing cost the members of a flying club plan to

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92. Sharing cost. The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more people to join the club so that the cost per person will decrease by $2000. How many mem- bers are currently in the club? Figure for Exercise 89 40 in. 30 in. x 93. Farmer’s Delight. The manager of Farmer’s Delight bought a load of watermelons for $750 and priced the watermelons so that he would make a profit of $2 on each melon. When all but 100 of the melons had been sold, he broke even. How many did he buy originally? 94. Traveling club. The members of a traveling club plan to share equally the cost of a $150,000 motorhome. If they can find 10 more people to join and share the cost, then the cost per person will decrease by $1250. How many members are there originally in the club? Getting More Involved 95. Discussion Find the solutions to 6 x 2 5 x 4 0. Is the sum of your solutions equal to b a ? Explain why the sum of the solutions to any quadratic equation is b a . ( Hint: Use the quadratic formula.) 96. Discussion Use the result of Exercise 95 to check whether 2 3 , 1 3 is the solution set to 9 x 2 3 x 2 0. If this solution set is not correct, then what is the correct solution set? 97. Discussion What is the product of the two solutions to 6 x 2 5 x 4 0? Explain why the product of the solutions to any quadratic equation is a c . 98. Discussion Use the result of the previous exercise to check whether 9 2 , 2 is the solution set to 2 x 2 13 x 18 0. If this solution set is not correct, then what is the correct solution set? Graphing Calculator Exercises Determine the number of real solutions to each equation by examining the calculator graph of y ax 2 bx c. Use the discriminant to check your conclusions. 99. x 2 6.33 x 3.7 0 100. 1.8 x 2 2.4 x 895 0 101. 4 x 2 67.1 x 344 0 102. 2 x 2 403 0 103. x 2 30 x 226 0 104. 16 x 2 648 x 6562 0 Figure for Exercise 88 Height (ft) Time (sec) 0 0 100 2 4 6 8 10 200 300 400 dug22241_ch10a.qxd 11/10/2004 18:30 Page 638
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10-23 10.3 Graphing Parabolas 639 Finding Ordered Pairs It is straightforward to calculate y when given x for an equation of the form y ax 2 bx c . However, if we are given y and want to find x , then we must use methods for solving quadratic equations. 10.3 Graphing Parabolas The graph of any equation of the form y mx b is a straight line. In this section we will see that all equations of the form y ax 2 bx c (with a 0) have graphs that are in the shape of a parabola. In this Section Finding Ordered Pairs Graphing Parabolas The Vertex and Intercepts Applications E X A M P L E 1 Finding ordered pairs Complete each ordered pair so that it satisfies the given equation. a) (2, ), ( , 0), y x 2 x 6 b) (0, ), ( , 20), y 16 x 2 48 x 84 Solution a) If x 2, then y 2 2 2 6 4. So the ordered pair is (2, 4). To find x when y 0, replace y by 0 and solve the resulting quadratic equation: x 2 x 6 0 ( x 3)( x 2) 0 x 3 0 or x 2 0 x 3 or x 2 The ordered pairs are ( 2, 0) and (3, 0).
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