MAC1105 Exam #3 Review PDF

# MAC1105 Exam #3 Review Packet ## Multiple Choice ### The graph of a quadratic function is given. Determine the function's equation. 1. - The graph is a parabola that opens upwards, the vertex is at (0, 3) - **Answer: B) g(x) = x² + 6x + 9** 2. - The graph is a parabola that opens do...

# MAC1105 Exam #3 Review Packet ## Multiple Choice ### The graph of a quadratic function is given. Determine the function's equation. 1. - The graph is a parabola that opens upwards, the vertex is at (0, 3) - **Answer: B) g(x) = x² + 6x + 9** 2. - The graph is a parabola that opens downwards, the vertex is at (0, -3) - **Answer: A) h(x) = -x² - 3** ### Find the coordinates of the vertex for the parabola defined by the given quadratic function. 3. f(x) = 4 - (x + 3)² - **Answers: D) (-3, 4)** 4. y + 9 = (x - 3)² - **Answers: C) (3, -9)** 5. f(x) = 3 - x² - 2x - **Answers: C) (-1, 4)** 6. f(x) = -3x² + 6x + 1 - **Answers: A) (2, -5)** ### Find the axis of symmetry of the parabola defined by the given quadratic function. 7. y + 9 = (x + 3)² - **Answers: D) x = -3** 8. f(x) = 4 - (x + 5)² - **Answers: A) x = -5** 9. f(x) = -x² + 14x + 4 - **Answers: D) x = 7** 10. f(x) = 5x² + 10x - 6 - **Answers: B) x = -1** ### Find the range of the quadratic function. 11. f(x) = 7 - (x + 2)² - **Answers: D) (-∞, 7]** 12. y + 9 = (x + 3)² - **Answers: C) [-9, ∞)** 13. f(x) = -x² - 8x - 9 - **Answers: D) (-∞, -4]** 14. f(x) = -3x² + 3x - **Answers: C) (-∞, (3/4)]** ### Find the x-intercepts (if any) for the graph of the quadratic function. 15. f(x) = 2x² - 6x - 20 - **Answers: D) (-2, 0) and (5, 0)** 16. f(x) = -x² + 17x - 72 - **Answers: C) (8, 0) and (9, 0)** ### Find the y-intercept for the graph of the quadratic function. 17. y + 9 = (x + 3)² - **Answers: D) (0, 6)** ### Find the domain and range of the quadratic function whose graph is described. 18. The minimum is -6 at x = -1. - **Answer: A) Domain: (-∞, ∞) Range: [-6, ∞)** 19. The vertex is (-1, -12) and the graph opens up. - **Answer: C) Domain: (-∞, ∞) Range: [-12, ∞)** ## Solve the problem. 20. Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 5x², but which has a minimum of 5 at x = 2. - **Answer: C) f(x) = 5(x - 2)² + 5** 21. Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = -7x², but which has a maximum of 8 at x = 4. - **Answer: D) f(x) = -7(x - 4)² + 8** 22. f(x) = 9 - (x - 3)² - **Answer: D)** ### Use the vertex and intercepts to sketch the graph of the quadratic function. 23. f(x) = -2x² + 20x - 49 - **Answer: B)** ### Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. 24. f(x) = 2x² - 4x - **Answer: B) minimum; (1, -2)** 25. f(x) = -x² - 2x - 8 - **Answer: A) maximum; (-1, -7)** ## Solve the problem. 26. A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 244 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? - **Answer: C) 7442 ft²** 27. A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 624 feet of fencing is used. Find the maximum area of the playground. - **Answer: B) 16,224 ft²** 28. The owner of a video store has determined that the cost C, in dollars, of operating the store is approximately given by C(x) = 2x² - 26x + 640, where x is the number of videos rented daily. Find the lowest cost to the nearest dollar. - **Answer: D) $556** 29. A person standing close to the edge on top of a 320-foot building throws a baseball vertically upward. The quadratic function s(t) = -16t² + 64t + 320 models the ball's height above the ground, s(t), in feet, t seconds after it was thrown. After how many seconds does the ball reach its maximum height? Round to the nearest tenth of a second if necessary. - **Answer: A) 2 seconds** ## Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation 30. x² - 3x - 28 < 0 - **Answer: C) (-4, 7)** 31. x² - 2x ≥ 8 - **Answer: D) (-∞, -2] [4, ∞)** 32. (x + 4)(x + 3)(x - 7) > 0 - **Answer: C) (-4, -3) υ (7,∞)** 33. x² + 7x ≤ -12 - **Answer: C) [-4, -3]** 34. 16x³ + 48x² - 25x - 75 > 0 - **Answer: B) (-3, -5/4) U (5/4, ∞)** ## Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 35. (-x + 8)/(x - 2) ≥ 0 - **Answer: D) (2, 8]** 36. (x + 5)(x - 2)/(x - 1) ≥ 0 - **Answer: B) [-5, 1) u [2, ∞)** 37. (x - 1)(3 - x)/(x - 2)² ≤ 0 - **Answer: C) (-∞, 1] U [3, ∞)** 38. (x + 9)/(x + 2) < 5 - **Answer: D) (-∞, -2) or (-4, ∞)** 39. 2x/(x + 6) < x - **Answer: C) (-6, -4) ∪ (0, ∞)** ## Solve the problem. 40. An arrow is fired straight up from the ground with an initial velocity of 240 feet per second. Its height, s(t), in feet at any time t is given by the function s(t) = -16t² + 240t. Find the interval of time for which the height of the arrow is greater than 116 feet. - **Answer: D) between 1/2 and 29/2 sec** 41. You drive 123 miles along a scenic highway and then take a 25-mile bike ride. Your driving rate is 4 times your cycling rate. Suppose you have no more than a total of 7 hours for driving and cycling. Let x represent your cycling rate in miles per hour. Write a rational inequality that can be used to determine the possible values of x. Do not simplify and do not solve the inequality. - **Answer: D) 123/4x + 25/x ≤ 7** ## Determine whether the given ordered pair is a solution of the system 42. (-5, -5) 4x = 15 - y 3x = -5 -4y - **Answer: B) not a solution** ## Solve the system of equations by the substitution method. 43. 3x - 2y = -28 - 3x 4x + 7y = x + 6y + -4 - **Answer: A) {(-3, 5)}** 44. 9x + 8y = 62 7x - 5y = 37 - **Answer: C) {(6, 1)}** ## Solve the system by the addition method. 45. 8x + 6y = 28 4x - 2y = 24 - **Answer: A) {(5, -2)}** 46. 6y = 63 - 7x 2x = 78 - 6y - **Answer: A) {(7, -14)}** ## Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 47. 3x + y = 11 9x + 3y = 33 - **Answer: C) {(x, y) | 3x + y = 11}** 48. 9x - 2y = 7 -27x + 6y = -14 - **Answer: D) Ø** 49. x/2 + y/4 = 1 y/2 - x = 0 - **Answer: D) { [18/4] }** 50. y = -5x - 4 -10x - 2y = 8 - **Answer: C) {(x, y) 1 5x + y = −4}** ## Solve the problem. 51. Steve invests in a circus production. The cost includes an overhead of $36,000, plus production costs of $5000 per performance. A sold-out performance brings in $8000. Let x represent the number of sold-out performances and write the cost function, C and revenue function, R. - **Answer: A) C(x) = 36,000 + 5000x R(x) = 8000x** 52. The Family Fine Arts Center charges $25 per adult and $15 per senior citizen for its performances. On a recent weekend evening when 502 people paid admission, the total receipts were $9330. How many who paid were senior citizens? - **Answer: D) 322 senior citizens** 53. A flat rectangular piece of aluminum has a perimeter of 70 inches. The length is 11 inches longer than the width. Find the width. - **Answer: B) 12 inches** 54. The rabbit population in a forest area grows at the rate of 9% monthly. If there are 160 rabbits in July, find how many rabbits (rounded to the nearest whole number) should be expected by next July. Use y = 160(2.7)0.09t - **Answer: A) 468** 55. The formula S = A * (1 + r)^t + 1 - 1 / r models the value of a retirement account, where A = the number of dollars added to the retirement account each year, r = the annual interest rate, and S = the value of the retirement account after t years. If the interest rate is 6%, how much will the account be worth after 15 years if $400 is added each year? Round to the nearest whole number. - **Answer: B) $10,269** ## The graph of an exponential function is given. Select the function for the graph from the functions listed. 56. The graph shows points (0,1), (-1, 3), (-2, 9) - **Answer: A) f(x) = -3x** 57. The graphs shows a curve that is increasing exponentially. - **Answer: B)** 58. The graph shows a decreasing exponential curve - **Answer: A) f(x) = 3x - 2** ## Solve the problem. 59. The population in a particular country is growing at the rate of 2.2% per year. If 6.365.000 people lived there in 1999, how many will there be in the year 2005? Use f(x) = ype^(0.022t) and round to the nearest ten-thousand. - **Answer: C) 7.260.000** ## Use the compound interest formulas *A = P(1 + r/n)^nt * and *A = Pe^(rt)* to solve 60. Suppose that you have $4000 to invest. Which investment yields the greater return over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually? - **Answer: B) $4000 invested at 6.25% compounded continuously over 10 years yields the greater return.** 61. Suppose that you have $10,000 to invest. Which investment yields the greater return over 9 years: 5.4% compounded monthly or 5.5% compounded quarterly? - **Answer: C) $10,000 invested at 5.5% compounded quarterly over 9 years yields the greater return.**