SECTION 3.5 Inequalities Involving Quadratic Functions 179 24. Challenge Problem Use the result obtained in Problem 22 to find the area enclosed by f x x2 8, 2 ( ) = + the x -axis, and the lines x 2 = − and x 2. = 25. Challenge Problem Use the result obtained in Problem 22 to find the area enclosed by f x x x3 5, 2 ( ) = + + the x -axis, and the lines x 4 = − and x 4. = 26. Challenge Problem Use the result obtained in Problem 22 to find the area enclosed by f x x x 4, 2 ( ) = − + + the x -axis, and the lines x 1 = − and x 1. = Show that this area may also be given by h y y y Area 3 4 0 1 2 ( ) = + + (h, y2) h 2h (2h, y0) (0, y1) x y 23. Challenge Problem Use the result obtained in Problem 22 to find the area enclosed by f x x5 8, 2 ( ) = − + the x -axis, and the lines x 1 = − and x 1. = ‘Are You Prepared?’ Answers 1. A r2 π = 2. y x 1.7826 4.0652 = + 27. Refer to Example 1 in this section. Notice that if the price charged for the calculators is $0 or $140, then the revenue is $0. It is easy to explain why revenue would be $0 if the price charged were $0, but how can revenue be $0 if the price charged is $140? Explaining Concepts Problems 28–37 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for subsequent sections, a final exam, or later courses such as calculus. 28. Find the distance between the points P 4, 7 1 ( ) = − and P 1, 5 . 2 ( ) = − 29. Find the equation of the circle with center 6, 0 ( ) − and radius r 7. = 30. Solve: x x 5 8 3 0 2 + − = 31. Find the x- intercept and y- intercept of the graph of x y 5 7 140. + = 32. Solve: − − = x 2 3 7 9 21 33. Find the quotient and remainder: x x x 7 19 15 3 2 − + − is divided by x 3 − 34. Find the domain of f x x x x 5 1 16 . 3 ( ) = − − 35. Find the function that is finally graphed after all three of the following transformations are applied to the graph of f x x 9 : 2 ( ) = − (1) Shift left 3 units (2) Vertical stretch by a factor of 2 (3) Shift down 4 units 36. Find the difference quotient of f f x x : 3 1 ( ) = − 37. Factor completely: x x x x 4 1 7 5 1 7 5 3 4 4 ( ) ( ) ( ) ( ) + − + + − Retain Your Knowledge OBJECTIVE 1 Solve Inequalities Involving a Quadratic Function (p. 180) 3.5 Inequalities Involving Quadratic Functions Now Work the ‘Are You Prepared?’ problems on page 182. • Solve Inequalities (Section A.9, pp. A80–A83) • Use Interval Notation (Section A.9, pp. A77–A78) PREPARING FOR THIS SECTION Before getting started, review the following:
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