Dalia Isabel Gonzalez rocha math1010spring2016-90 3 WeBWorK assignment number WBWK-12 is due : 04/11/2016 at 11:59pm MDT. These are Quadratic Equations. Solve them. The early bird gets the worm, but the second mouse gets the cheese! The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are having trouble guring out your error, you should consult the book, or ask a fellow student, one of the TA's or your professor for help. Don't spend a lot of time guessing - it's not very efcient or effective. Give 4 or 5 signicant digits for (oating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2 ^ 3 instead of 8, sin(3 pi/2)instead of -1, e ^ (ln(2)) instead of 2, (2 + tan(3)) (4 sin(5)) ^ 6 7/8 instead of 27620.3413, etc. Here's the list of the functions which WeBWorK understands. You can use the Feedback button on each problem page to send e-mail to the professors. 1. (3 pts) There are different ways to write a quadratic function. Each way corresponds to a specic piece of information in the graph. Find the following information. It should take you very little work to do this ... if your not sure how, ask! Each table represents a linear or quadratic function, or a function that is neither. Identify whether each table is linear, quadratic, or neither and write a sentence explaining how you know. Table A A) Standard form: f (x) = 2x2 + 49x + 61 x 1 0 1 2 y-intercept: Completed-Square form: f (x) = 19(x + 18)2 72 f (x) 1.5 2 3 5 The function is ? , because ... vertex: Table B Factored form form: f (x) = 2(x + 3)(x x-intercepts: 16) x 1 0 1 2 , Note: Enter x-intercept with smaller x-coordinate rst, with larger x-coordinate second. f (x) 4 3 4 7 The function is ? , because ... 2. (1 pt) USE THE APPLICATIONS OF QUADRATICS WORKSHEET WHEN COMPLETING THIS PROBLEM. Table A x 1 0 1 2 This problem is from the worksheet that accompanies the Webwork 12 problems. There are some aspects - like graphing and justifying your answers, which are important to do, but can not be assessed in Webwork. You should print out the worksheet, complete it, and transfer your answers here. Solutions to the worksheet will be posted after the Webwork deadline. f (x) 3 1 1 3 The function is ? , because ... 1 3. (1 pt) Match each graph with its corresponding equation. ? ? ? ? 1. (x + 2)2 3 2. (x + 2)2 + 3 3. (x 2)2 + 3 4. (x + 2)2 3 A B C D E F (Click on a graph to enlarge it) A B C 5. (1 pt) D E The quadratic function in the graph is given by f (x) = a(x h)2 +k. From the graph, determine whether each constant a, h, and k is positive, negative, or zero. F (Click on a graph to enlarge it) a is ? h is ? k is ? 4. (1 pt) Match the each graph with its corresponding equation. ? 1. (x 3)2 + 2 ? 2. (x + 3)2 2 ? 3. (x + 2)2 + 3 ? 4. (x 3)2 + 2 2 6. (1 pt) Similarly, the graph in this Figure Write f(x) in completed square form to determine how the vertex (and hence the function) is shifted: The parent function for this type of function is: g(x) = The function g(x) was shifted to the left and to obtain f (x). The axis of symmetry of the function f (x) is x = . up . 9. (1 pt) The graph in this Figure is the graph of the function g(x) = Hint: Ask what happens to the vertex of the graph. 7. (1 pt) The graph in this Figure is obtained from that of f (x) = x2 by a combination of scaling and shifting: is the graph of the function g(x) = Hint: Ask what happens to the vertex of the graph. 10. (2 pts) For the graph of the equation y = x2 36, draw a sketch of the graph on a piece of paper. Then answer the following questions: The x-intercept(s) is(are): Note: If there is more than one answer enter them separated by commas (i.e.: (1,2),(3,4)). If there are none, enter none . The y-intercept(s) is (are): Note: If there is more than one answer enter them separated by commas (i.e.: (1,2),(3,4)). If there are none, enter none . It is the graph of the function g(x) = Hint: Figure out the scale by going one unit to the right from the vertex, and see what happens to the function value. Consider the location of the vertex. The axis of symmetry is: 8. (1 pt) Suppose you have a quadratic function g(x) with vertex at (0, 0). You shift it horizontally and vertically and obtain the function f (x) = x2 + 4x + 11. . Note: you must answer all questions correctly to get credit for this problem. 3 11. (2 pts) Put the function y = 6x2 + 24x + 11 in vertex form f (x) = a(x h)2 + k and determine the values of a, h, and k. HINT: Use completing the square to rewrite the function so that it is in a form that is easy to graph. Then graph the function and answer the question. a= h= 16. (2 pts) Use what you know aboutp graphs of quadratic the functions to nd the domain of f (x) = (x 4)(x + 2). Enter your answer using inequalities. k= 12. (3 pts) Given the function f (x) = 3x2 + 26x 35, algebraically determine the vertex, x-intercepts, and y-intercept. Its vertex is ( , ). Its x-intercepts are . Note: If there is more than one answer enter them separated by commas (i.e.: (1,2),(3,4)). 17. (1 pt) Find the minimum and maximum value of the function y = (x 3)2 + 7. Enter innity or -innity if the function never stops increasing or decreasing. Its y-intercept is Maximum value = . 13. (2 pts) Suppose y = 3x2 + 30x 78. In each part below, if there is more than one correct answer, enter your answers as a comma separated list. If there are no correct answers, enter NONE. Minimum value = 18. (2 pts) The height of a triangle is 25 inches greater than its base. The area of the triangle is 625 square inches. The height of the triangle is inches and the base of the triangle is inches. Hint: The area of a triangle equals one half of base times height. (a) Find the y-intercept(s). y= (b) Find the x-intercept(s). x= 14. (2 pts) Use completing the square to rewrite the function f (x) = 5x2 + 2x 7 in the form f (x) = a(x h)2 + k. Find the axis of symmetry: 19. (2 pts) A rectangular lawn has a length that is 4 yards greater than the width. The area of the lawn is 77 square yards. Note: The formula for the area of a rectangle is Area = length width . a) Write the polynomial equation for the area of the lawn. Use the variable x to represent the width of the lawn. x= Answer: b) Solve the equation and give the width of the lawn. Does the graph face up, down, or neither? Type in your answer as UP, DOWN, or NEITHER . NOTE: State the units in your answer. Answer: 15. (2 pts) Suppose f (x) = x2 Width: 11x + 18. (a) For which values of x is the function f (x) positive? Enter your answer using inequalities. 20. (2 pts) A rectangle has an area of 220 cm2 and a perimeter of 62 cm. What are its dimensions? Its length is Its width is (a) For which values of x is the function f (x) negative? Enter your answer using inequalities. 4 E) The time when the ball is at its highest. ? 23. (1 pt) You are given a scenario which can be modeled by a quadratic function. Each part of the scenario corresponds to a different part of the graph of the quadratic function. Choose the part of the graph that gives information about the specied part of the scenario. SCENARIO: A publishing house has printed 10,000 copies of a book and is deciding what price they should sell the book at. If the price is low, they sell many copies, but make little or no prot on them. If the price is high, the prot on each book is substantial, but the do not sell many copies. The following model describes the prot which the publishing house earns if the price of the book is given by x dollars. 21. (1 pt) The Food Stamp Program is America's rst line of defense against hunger for millions of families. Over half of all participants are children; one out of six is a low-income older adult. The function, f (x), models the number of people, in millions, receiving food stamps x years after 1990. Use the graph of f (x) given above to estimate the answers to the following questions. a) How many million people received food stamps in the year 1998? Answer: million b) In which year(s) did 19.75 million people receive food stamps? Note: If there are more than one year, enter the years separated with a comma. Width: 22. (1 pt) You are given a scenario which can be modeled by a quadratic function. Each part of the scenario corresponds to a different part of the graph of the quadratic function. Choose the part of the graph that gives information about the specied part of the scenario. f (x) = 60x2 1740x 940 Parts of the scenario: A) The price which maximizes the prot. ? B) The amount they lose if they give the book away for free. ? C) The largest possible prot. ? D) The price at which the publisher goes from losing to making money. ? E) The price at which the publisher goes from making to losing money. ? 24. (2 pts) A coin, thrown upward at time t = 0 from an ofce in the Empire State Building, has height in feet above the ground t seconds later given by h(t) = 16t 2 + 96t + 432 = 16(t 9)(t + 3). (a) From what height is the coin thrown? Include units in your answer. SCENARIO: The height of a baseball t seconds after being hit is modeled by: h(t) = 16t 2 + 75t + 3.5 Parts of the scenario: (b) At what time does the coin hit the ground? Include units in your answer. 25. (3 pts) At time t = 0, in seconds, a pair of sunglasses is dropped from the Eiffel Tower in Paris. At time t, its height in feet above the ground is given by h(t) = 16t 2 + 1000. A) The height of the ball when it is hit. ? B) The time when the ball hits the ground. ? C) A part of the graph unrelated to the scenario. ? (a) What does the function tell us about the height from which the sunglasses were dropped? Include units in your answer. D) The maximum height of the ball. ? 5 27. (3 pts) USE THE APPLICATIONS OF QUADRATICS WORKSHEET WHEN COMPLETING THIS PROBLEM. (b) When do the sunglasses hit the ground? Include units in your answer. This problem is from the worksheet that accompanies the Webwork 12 problems. There are some aspects - like graphing and justifying your answers, which are important to do, but can not be assessed in Webwork. You should print out the worksheet, complete it, and transfer your answers here. Solutions to the worksheet will be posted after the Webwork deadline. 26. (4 pts) USE THE APPLICATIONS OF QUADRATICS WORKSHEET WHEN COMPLETING THIS PROBLEM. This problem is from the worksheet that accompanies the Webwork 12 problems. There are some aspects - like graphing and justifying your answers, which are important to do, but can not be assessed in Webwork. You should print out the worksheet, complete it, and transfer your answers here. Solutions to the worksheet will be posted after the Webwork deadline. A ball is thrown up on the surface of a moon. Its height above the lunar surface (in feet) after t seconds is given by the formula We want to build a pen for sheep and we have fty feet of fencing. We plan to build the pen next to the river so that we only need to include 3 sides. See the picture on the worksheet. a. If L = 5, then W = If L = 10, then W = . h = 429t a. Graph your function. (Hint you could use the techniques developed in Section 8.4.) Also, you can use a standard calculator, but do not use a graphing calculator. Enter your answers on the worksheet. . b. (on worksheet) b. Where on the graph can you nd the information about the maximum height? ? c. Write the width W as a function of the length L. The width W= . d. If L = 5, then A = If L = 10, then A = . 13 2 t . 4 c. Find the time that the ball reaches its maximum height. Answer = . d.Find the maximal height attained by the ball Answer = 28. (2 pts) A rancher has 208 feet of fencing to enclose a coral and run a fence down the middle of the coral dividing it into two parts. What dimensions will produce the largest total area? (Hint: Find a function for the area and use the properties of the related graph to determine the maximum area). e. Write the area A as a function of the length L. The area A= . f. What choice of L maximizes the area? L = ft Your answer is: separated by commas.) g. (on worksheet) feet. (Enter length and width What is the maximum total area? h. What is the maximum area? A = sq ft Your answer is: Generated by c WeBWorK, http://webwork.maa.org, Mathematical Association of America 6 square feet. APPLICATIONS: QUADRATICS This is a series of problems in which you will apply the ideas you worked with this week. You should print out the handout for this problem write your work and answers here and then transfer what is asked for into Webwork. There are some aspects - like graphing and justifying your answers, which are important to do, but can not be assessed in Webwork. Compare your work on these to the solutions, which be posted after Webwork is deadline. 1. (This is problem 2 in WeBWorK) Each table represents a linear or quadratic function, or a function that is neither. Identify whether each table is linear, quadratic, or neither and write a sentence explaining how you know. (Hint: you might look at the graph to try to spot quadratics or lines, or compare slopes.) Table A x f(x) -1 1.5 0 2 1 3 2 5 Table B x f(x) -1 4 0 3 1 4 2 7 Table C x f(x) -1 3 0 1 1 -1 2 -3 Table A is (circle one): linear quadratic neither because: Table B is (circle one): linear quadratic neither because: Table C is (circle one): linear quadratic neither because: ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ 2. Sheep Pen. (This is problem 26 on webwork) We want to build a pen for sheep and we have fifty feet of fencing. We plan to build the pen next to the river so that we only need to include 3 sides, as shown in the picture: a. Make a table for values of L and W. Two values of L are given. Find 3 more. L W d. Make a table of L and the area A. L A 5 5 10 10 e. Write A as a function of the length L. b. Graph the width W as a function of L. f. What choice of L maximizes the area? g. Explain how you found the answer in f. c. Write the width W as a function of the length L. h. What is the maximum area? 3. Moon Problem. (This is problem 27 on webwork) A ball is thrown up on the surface of a moon. Its height above the lunar surface (in feet) after t seconds is given by the formula (see your individual webwork problem.) a. Graph your function. (Hint - you could use the techniques developed in Section 8.4.) Also, you can use a standard calculator, but do not use a graphing calculator. b. Where on the graph can you find the information about the maximum height? c. Find the time that the ball reaches its maximum height. d. Find the maximal height attained by the ball