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Math 1090.04 Exam 02 Spriig 2013 orrn A Student ID Number: Name Instructions: • Please remove headphones and hats during the exam • Show all work, as partial credit will be given where appropriate. If no work is shown, there may be no credit given. • All final answers should be written in the space provided on the exam and in simplified form. When needed give your answer as an exact amount, , except for dollar amounts 2 i.e., a fraction or symbolic expression like e which should be rounded to the nearest cent. • CALCULATORS ARE NOT ALLOWED ON THIS EXAM • This is a “closed notes/closed book” exam You are not allowed any outside aids during this exam. If you have papers at your desk during the exam you will be given a zero on the exam. - • If your phone is out during the exam it will be considered a cheating offense put your phone away! - 22 March 2013 Exam 02, Page 2 of 10 MathlO9O.004 WRITE YOUR ANSWERS ON THE LINES PROVIDED 1. 2 + bx + c (a) Suppose you are given the equation ax for finding the solutions to this equation. = 0. Write the quadratic formula C — 2 (b) Solve using any method: 3x — 16x + 5 = 0 ,77e1)-L,o/: 3-5=)5 (_i)(-i)z / Sy 3 i 2 = J)(= 2. Fred has $150,000 to invest in three different mutual funds. He wishes to invest this money and make an Zprofit over the next year. Over the last year, the first fund has had a return of 5%, the second fund has had a return of 9%, while the third fund has had a return of 12%. Fred likes the second fund, so he wishes to invest $10,000 more in the second fund than in the third fund. How much should he invest in each company to make 8% return on the $1S0,000? Write the system of equations described by this system DO NOT SOLVE 00 O Gri-e utç16&j: 3 9e = m oun x in oninI - 3OOOO /ooooO /5O,000 [email protected]±.’ j:: 2-t-/0 00o 1 .o(,o,ooô J30O C 1 22 March 2013 Exam 02, Page 3 of 10 MathlO9O.004 3. Graph the parabola described by the following equation: f(x) 2 + —8x + 1. —2x (a) Transform this equation from standard form to “parabola form” by Completing the Square: (—2-c (x= )41 - (k72 =_(y2K = )÷/+ -2(y+9 9] (b) Based on the standard form and parabola form of the given equation, fill in the information below: ; a Coefficients: c Vertex: (x,y)= Axis of Symmetry: x y-intercept (,y)= (ô = = — 2; h = k — 9) = ) Concave Up or Concave Down? Vertex a Max or Mm? Stretched or Shrunk Lengthwise? Width 2 Location y Width 4 Location y a = 1(-) / Exam 02, Page 4 of 10 Math 1090.004 22 March 2013 (c) Graph the parabola and axis of symmetry on the coordinate plane below: / (- — - — - zz zz: z:ziz. :i: — — — ——- — - c — — / I I - - i..— — — — — — — - - wc1ti4 I ———————H z:Z:±:zizz::t: 0 C Exam 02, Page 5 of 10 MathlO9O.004 22 March 2013 4. Given the revenue and cost functions below: R(w) C(w) = = —w + 1600w 2 1500w 1600 -- where w is the quantity of units produced and sold. (a) What is the maximum profit? 0 - QQWtILQO 2 =-W toow —(W 2 [-sop (vvz_Ioow - VLx: Ioo 4DO * 0 (w- 4tco 4)00 rriiwrnpo:f1- (b) How many units must be sold to obtain this maximum profit? o6/v-’n u !YL&Xjfl’LLLIy) pi-oi± OO 22 March 2013 Exam 02, Page 6 of 10 MathlO9O.004 5. Given the following rational function: f(x) answer the following questions: = [ 1 poin X (a) What is the Domain of this function? ) (b) What are the Roots of this function? 3)<+ — - - ox-I (c) What is the y - intercept of this function? __L (d) “Limits”: — . 0 As-oo:f(x) (e) “Events”: What are the x values of the “Events” described by this system? tJ (f) Graph these events on a number line below and determine whether the function is positive or negative in each region. SHOW YOUR WORK J 0 —---s &(-IO1 O) Exam 02, Page 7 of 10 1\Iath1090.004 6. Based on your answers to the questions above: (a) What are the vertical asymptotes, if any, of this system? V I,.— (b) What are the horizontal asymptotes,if any, of this system? 3 Ii -: t 2 /L (c) In what region(s) is the function positive? 6(-OO,-k) (/2 (d) In what regions(s) is the function negative? 6 (-/3) ) 7. Now that you have answered the questions above, graph the function: 1[*ZZL :: vJ. x 22 March 2013 Exam 02, Page 8 of 10 MathlO9O.004 22 IVIarch 2013 8. Graph the following piecewise function on the coordinate plane below: ( f(x) = 2x — 2 —-x—+ n i x>4 -x<4 x<-Z 0 C C MathlO9O.004 Exam 02, Page 9 of 10 Intentionally Left Blank 22 March 2013 MathlO9O.004 Exam 02, Page 10 of 10 Scratch Paper 22 March 2013 ç 0 0