Chapter Review 185 In Problems 6–8, graph each quadratic function using transformations (shifting, compressing, stretching, and/or reflecting). 6. f x x 1 4 2 ( ) ( ) = + − 7. f x x 4 2 ( ) ( ) = − − 8. f x x 3 2 1 2 ( ) ( ) = − + + In Problems 9–13, (a) graph each quadratic function by determining whether its graph is concave up or is concave down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any. (b) Determine the domain and the range of the function. (c) Determine where the function is increasing and where it is decreasing. 9. f x x 2 2 2 ( ) ( ) = − + 10. f x x 1 4 16 2 ( ) = − 11. f x x x 4 4 2 ( ) = − + 12. f x x x 9 2 3 1 2 ( ) = + + 13. f x x x 3 4 1 2 ( ) = + − In Problems 14–16, determine whether the given quadratic function has a maximum value or a minimum value, and then find the value. 14. f x x x 3 6 4 2 ( ) = − + 15. f x x x8 4 2 ( ) = − + − 16. f x x x 3 12 4 2 ( ) = − + + In Problems 17 and 18, solve each quadratic inequality. 17. x x6 16 0 2 + − < 18. x x 3 14 5 2 ≥ + In Problems 19 and 20, find the quadratic function for which: 19. Vertex is 2, 4 ; ( ) − y-intercept is 16 − 20. Vertex is 1, 2 ; ( ) − contains the point 1, 6 ( ) 21. Sales Commissions Orlando was just offered a sales position for a computer company. His salary would be $25,000 per year plus 1% of his total annual sales. (a) Find a linear function that relates Orlando’s annual salary, S, to his total annual sales, x. (b) If Orlando’s total annual sales were $1,000,000, what would be Orlando’s salary? (c) What would Orlando have to sell to earn $100,000? (d) Determine the sales required of Orlando for his salary to exceed $150,000. 22. Demand Equation The price p (in dollars) and the quantity x sold of a certain product satisfy the demand equation x p 1500 10 = − (a) Find a model that expresses the revenue R as a function of the price p. (b) What is the domain of R? Assume R is nonnegative. (c) What unit price should be used to maximize revenue? (d) If this price is charged, what is the maximum revenue? (e) How many units are sold at this price? (f) What price should be charged to collect at least $56,000 in revenue? 23. Landscaping A landscape engineer has 200 feet of border to enclose a rectangular pond. What dimensions will result in the largest pond? 24. Enclosing the Most Area with a Fence A farmer with 10,000 meters of fencing wants to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. See the figure. What is the largest area that can be enclosed? 25. Architecture A special window in the shape of a rectangle with semicircles at each end is to be constructed so that the outside perimeter is 100 feet. See the illustration. Find the dimensions of the rectangle that maximizes the area of the rectangle. 26. Minimizing Marginal Cost Callaway Golf Company has determined that the marginal cost C of manufacturing x Top Flight golf clubs may be expressed by the quadratic function C x x x 4.9 617.4 19,600 2 ( ) = − + (a) How many clubs should be manufactured to minimize the marginal cost? (b) At this level of production, what is the marginal cost? 27. Maximizing Area A rectangle has one vertex on the line y x x 10 , 0, = − > another at the origin, one on the positive x-axis, and one on the positive y-axis. Express the area A of the rectangle as a function of x. Find the largest area A that can be enclosed by the rectangle. 28. Parabolic Arch Bridge A horizontal bridge is in the shape of a parabolic arch. Given the information shown in the figure, what is the height h of the arch 2 feet from shore? 10 ft h 2 ft 20 ft 29. Bone Length Research performed at NASA, led by Dr. Emily R. Morey-Holton, measured the lengths of the right humerus and right tibia in 11 rats that were sent to space on Spacelab Life Sciences 2. The data shown on the next page were collected. (a) Draw a scatter plot of the data, treating length of the right humerus as the independent variable.
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