MATH 115 QUIZ 2 NAME: _______________________________ March-April, 2016 Instructor: S. Sands I have completed this assignment myself, working independently and not consulting anyone except the instructor. INSTRUCTIONS The quiz is worth 100 points. There are 13 problems. This quiz is open book and open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission). You may take as much time as you wish, provided you turn in your quiz no later than Sunday, April 3. Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. In your document, be sure to include your name and the assertion of independence of work. General quiz tips and instructions for submitting work are posted in the Quizzes module. If you have any questions, please contact me by e-mail. 1. (3 pts) Which of the following equations does the graph represent? (no explanation required) 1. ______ A. 2 y= x +4 3 B. 3 y= x +4 2 C. y= 3 x+ 4 2 D. y= 2 x+ 4 3 2. (10 pts) Consider the points (-5, -2) and (-1, 4). (a) Find the slope-intercept equation of the line passing through the two given points. Show work. (b) Graph the line you found in (a), either drawing it on the grid in the previous problem #1, or generating the graph electronically and attaching it. (c) Compare your line for this problem, #2, with the line in the previous problem #1. Are the two lines parallel, perpendicular, or neither parallel nor perpendicular? (The terms parallel and perpendicular are discussed on pages 166 and 167.) No explanation required - just state your answer. 3. (7 pts) Mike wants to purchase custom-made pens to advertise his business. Custom Products, Inc. offers the following deal: Pay a design fee of $15.00, plus $0.24 per pen (a) State a linear function f (x) that represents Custom Products' total charge for an order of x pens. (b) Mike wants to purchase 140 custom-made pens. What is the total charge? Show work/explanation. (c) If the total charge is $139.80, how many pens were ordered? Show work/explanation. 4. (8 pts) Look at the graph of the quadratic function and complete the table. Fill in the blanks Graph [No explanations required.] Equation (a) State the vertex: (d) The graph represents ____________ (b) State the range: which of the following equations? Choice:____ _____________ (c) State the interval on which the function is increasing: _____________ 5. (10 pts) Look at the graph of the polynomial function and complete the table. Graph A. y = -x2 + 2x - 2 B. y = -2x2 + x - 2 C. y = 2x2 - 3x - 2 D. y = x2 - 2x - 2 [No explanations required.] Fill in the blanks (a) Estimate the y-intercept value: _________ (b) Is the degree of the polynomial odd or even? (choose one) (c) Is the leading coefficient of the polynomial positive or negative? (choose one) (d) The graph represents which of the following polynomials, shown in factored form? Choice:____ A. f (x) = - 0.25 (x + 1)2 (x - 3/2) (x -4) B. f (x) = C. f (x) = - 0.25 (x + 1) (x - 3/2) (x -4) D. f (x) = 0.25 (x + 1)2 (x - 3/2) (x -4) 0.25 (x + 1) (x - 3/2) (x -4) (e) State the real-number zeros: ___________________ 6. (6 pts) The amount of home heating oil h in gallons in a tank t days after a fill-up is modeled by h(t) = -0.08t2 - 3t + 275 for 0 t 10. Find and interpret the average rate of change of h over the interval [0, 10]. Show work. 7. (7 pts) Let f (x) = | 5 - 2x |. [No explanations required.] (a) Which of the following is the graph of this function? Graph A Graph B Graph C (b) Solve | 5 - 2x | > 9 and write interval notation for the solution set. (no explanation required) A. B. C. D. (-, -2) (7, ) (-2, ) (-, 7) (-2, ) (-2, 7) Graph D #7(b)._______ 8. (4 pts) Solve the inequality x2 2x and write the solution set in interval notation. (no explanation required) A. B. C. D. 8. ______ (-, 2] (-, 0] [2, ) (-, 2] [0, ) [0, 2] 9. (4 pts) For f (x) = x3 - 3x2 - 8, use the Intermediate Value Theorem to determine which interval must contain a zero of f. (no explanation required) 9. _______ A. Between 0 and 1 B. Between 1 and 2 C. Between 2 and 3 D. Between 3 and 4 10. (5 pts) For z = 6 + 7i and w = 5 2i, find zw. That is, determine (6 + 7i)(5 2i) and simplify as much as possible, writing the result in the form a + bi, where a and b are real numbers. Show some work. 11. (8 pts) Consider the equation 5x2 + 5 = 8x. Find the complex solutions (real and non-real) of the equation, and simplify as much as possible. Show algebraic work. 12. (10 pts) Based on data retrieved from http://www.erh.noaa.gov/lwx/climate/dca/dcatemps.txt the following chart of Washington, DC yearly average temperatures has been prepared. Washington DC Avg Temp 64 62 60 58 56 Average Temperat ure (degrees) f(x) = 0.03x - 10.11 R = 0.62 54 52 50 48 46 1860 1880 1900 1920 1940 1960 1980 2000 2020 Year The line of best fit, the regression line, is y = 0.0344x - 10.107, where x = year and y = average Washington, DC temperature, in degrees. (a) Use the regression line to estimate the average Washington, DC temperature in 1888, to the nearest tenth of a degree. Show some work. (b) Use the regression line to estimate the average Washington, DC temperature in 2010, to the nearest tenth of a degree. Show some work. (c) What is the slope of the regression line? In a sentence, interpret what the slope is telling us, in the context of this real-world application. (d) In what year (to the nearest year) does the regression line predict an average Washington, DC temperature of 62.0 degrees? Show work, solving an appropriate equation. 13. (18 pts) The cost, in dollars, for a company to produce x widgets is given by C(x) = 3600 + 5x for x 0, and the price-demand function, in dollars per widget, is p(x) = 45 0.04x for 0 x 1125. In Quiz 1, problem #9(d), we saw that the profit function for this scenario is P(x) = ______________________________. (fill in with the profit function given in the Quiz 1 solutions) (a) The profit function is a quadratic function and so its graph is a parabola. Does the parabola open up or down? __________ (b) Find the vertex of the profit function P(x) using algebra. Show algebraic work. (c) State the maximum profit and the number of widgets which yield that maximum profit: The maximum profit is _______________ when ____________ widgets are produced and sold. (d) Determine the price to charge per widget in order to maximize profit. (e) Find and interpret the break-even points. Show algebraic work