Linear and Quadratic Functions. 2.1 Properties of Linear Functions. 1 Graph a Linear Function

Transcription

1 Ch. Linear and Quadratic Functions.1 Properties of Linear Functions 1 Graph a Linear Function MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the slope and -intercept of the function. 1) f() = - A) m = ; b = - B) m = ; b = C) m = -; b = - D) m = -; b = ) h() = -1-4 A) m = -1; b = - 4 B) m = 1; b = 4 C) m = 1; b = - 4 D) m = -1; b = 4 3) p() = A) m = -1; b =3 B) m =1; b = - 3 C) m = -1; b = - 3 D) m = 0; b = 3 4) f() = A) m = ; b = - 1 B) m = - 1 ; b = C) m = ; b = 1 D) m = 7 3 ; b = 1 ) F() = 8 A) m = 0; b = 8 B) m = 8; b = 0 C) m = 0; b = 0 D) m = 8; b = 8 6) G() = - A) m = -; b = 0 B) m = ; b = 0 C) m = - 1 ; b = 0 D) m = 0; b = - 7) F() = 1 A) m = 1 ; b = 0 B) m = ; b = 0 C) m = - 1 ; b = 0 D) m = 0; b = 1 Use the slope and -intercept to graph the linear function. 8) f() = Page 1

2 A) B) C) D) Page

3 9) g() = A) B) C) D) Page 3

4 ) p() = A) B) C) D) Page 4

5 11) f() = A) B) C) D) Page

6 1) h() = A) B) C) D) Page 6

7 13) F() = A) B) C) D) Page 7

8 14) G() = A) B) C) D) Page 8

9 1) F() = A) B) C) D) Determine whether the given function is linear or nonlinear. 16) = f() A) linear B) nonlinear Page 9

10 Use Average Rate of Change to Identif Linear Functions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the average rate of change for the function. 1) f() = A) 11 B) -8 C) 8 D) -11 ) h() = A) -7 B) 7 C) 8 D) -8 3) p() = A) -1 B) 1 C) - 4 D) 4 4) F() = -6 A) 0 B) C) 6 D) -6 ) f() = A) 3 B) - 3 C) 1 D) - 1 6) h() = A) - 3 B) 3 C) -3 D) 3 Page

11 3 Determine Whether a Linear Function is Increasing, Decreasing, or Constant MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the function. State whether it is increasing, decreasing, or constant.. 1) f() = A) increasing B) increasing C) decreasing D) increasing Page 11

12 ) g() = A) increasing B) increasing C) decreasing D) decreasing Page 1

13 3) h() = A) decreasing B) decreasing C) increasing D) increasing Page 13

14 4) h() = A) decreasing B) decreasing C) increasing D) increasing Page 14

15 ) p() = A) decreasing B) increasing C) increasing D) decreasing Page 1

16 6) f() = A) increasing B) decreasing C) increasing D) increasing Page 16

17 7) h() = A) decreasing B) increasing C) decreasing D) decreasing Page 17

18 8) F() = A) constant B) constant C) constant D) decreasing Find the Zero of a Linear Function MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the zero of the linear function. 1) f() = + 9 A) -9 B) 9 C) 0 D) 18 ) g() = A) 8 B) -8 C) 0 D) -16 Page 18

19 3) h() = 11 - A) 11 B) -11 C) 1 D) - 4) f() = A) -3 B) 3 C) 0 D) 18 ) g() = - 4 A) B) - C) 0 D) -4 6) h() = -4 + A) 4 B) - 4 C) 1 D) -1 7) F() = A) 4 B) 8 3 C) D) -4 8) G() = A) -40 B) 8 C) - 8 D) 40 Solve the problem. 9) Suppose that f() = and g() = - 1. (a) Solve f() = 0. (b) Solve g() = 0. (c) Solve f() = g(). A) (a) = -6; (b) = 1; (c) = 4. B) (a) = -6; (b) = 1; (c) = -. C) (a) = 6; (b) = 1; (c) = 4. D) (a) = -6; (b) = -1; (c) = 4. ) Suppose that f() = and g() = (a) Solve f() > 0. (b) Solve g() > 0. (c) Solve f() g(). A) (a) < -6; (b) > 16; (c) B) (a) < -6; (b) < 16; (c) -11 C) (a) > 6; (b) > 16; (c) > D) (a) < -6; (b) < -16; (c) Page 19

20 11) Let f() be the function represented b the dashed line and g() be the function represented b the solid line. Solve the equation f() = g() A) = B) = 3 C) = - D) = -3 1) Let f() be the function represented b the dashed line and g() be the function represented b the solid line. Solve the equation f() < g() A) > 1 B) < 1 C) > -3 D) < -3 13) Let f() be the function represented b the dashed line and g() be the function represented b the solid line. Solve the equation f() g() A) 1 B) 1 C) - D) < - Page 0

21 Work with Applications of Linear Functions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) A truck rental compan rents a moving truck one da b charging $39 plus $0.07 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number of miles driven. What is the cost of renting the truck if the truck is driven 1 miles? A) C() = ; $46.70 B) C() = ; $ C) C() = ; $39.77 D) C() = ; -$31.30 ) Linda needs to have her car towed. Little Town Auto charges a flat fee of $60plus $ per mile towed. Write a function epressing Lindaʹs towing cost, c, in terms of miles towed,. Find the cost of having a car towed miles. A) c() = + 60; $70 B) c() = ; $ C) c() = + 60; $60 D) c() = ; $6 3) To convert a temperature from degrees Celsius to degrees Fahrenheit, ou multipl the temperature in degrees Celsius b 1.8 and then add 3 to the result. Epress F as a linear function of c. A) F(c) = 1.8c + 3 B) F(c) = c C) F(c) = 33.8c D) F(c) = c ) If an object is dropped off of a tower, the velocit, V, of the object after t seconds can be obtained b multipling t b 3 and adding to the result. Epress V as a linear function of t. A) V(t) = 3t + B) V(t) = 3 + t C) V(t) = 4t D) V(t) = t - 3 ) If an object is dropped from a tower, then the velocit, V (in feet per second), of the object after t seconds can be obtained b multipling t b 3 and adding to the result. Find V as a linear function of t, and use this function to evaluate V(8.6), the velocit of the object at time t = 8.6 seconds. A) V(8.6) = 8. feet per second B) V(8.6) = 86. feet per second C) V(8.6) = 84. feet per second D) V(8.6) = 83. feet per second 6) The cost for labor associated with fiing a washing machine is computed as follows: There is a fied charge of $30 for the repairman to come to the house, to which a charge of $3 per hour is added. Find an equation that can be used to determine the labor cost, C(), of a repair that takes hours. A) C() = B) C() = C) C() = ( ) D) C() = ) In a certain cit, the cost of a tai ride is computed as follows: There is a fied charge of $.1 as soon as ou get in the tai, to which a charge of $1.90 per mile is added. Find an equation that can be used to determine the cost, C(), of an -mile tai ride. A) C() = B) C() = C) C() = 4.0 D) C() =. 8) In a certain cit, the cost of a tai ride is computed as follows: There is a fied charge of $.40 as soon as ou get in the tai, to which a charge of $1.90 per mile is added. Find an equation that can be used to determine the cost, C(), of an -mile tai ride, and use this equation to find the cost of a 6-mile tai ride. A) $13.80 B) $13.98 C) $13.68 D) $14.70 Page 1

22 9) Martʹs Tee Shirt & Jacket Compan is to produce a new line of jackets with an embroider of a Great Prenees dog on the front. There are fied costs of $80 to set up for production, and variable costs of $46 per jacket. Write an equation that can be used to determine the total cost, C(), encountered b Martʹs Compan in producing jackets. A) C() = B) C() = C) C() = ( ) D) C() = ) Martʹs Tee Shirt & Jacket Compan is to produce a new line of jackets with a embroider of a Great Prenees dog on the front. There are fied costs of $60 to set up for production, and variable costs of $46 per jacket. Write an equation that can be used to determine the total cost, C(), encountered b Martʹs Compan in producing jackets, and use the equation to find the total cost of producing 86 jackets. A) $476 B) $488 C) $46 D) $468 11) Suppose that the quantit supplied S and quantit demanded D of baseball caps at a major league game are given b the functions S(p) = 940-0p and D(p) = 1p, where p is the price. Find the equilibrium price for caps at the game. Then find the equilibrium quantit. A) $14, $140 B) $, $1940 C) $6, $340 D) $, $140 1) Regrind, Inc. regrinds used tpewriter platens. The variable cost per platen is $1.90. The total cost to regrind 0 platens is $300. Find the linear cost function to regrind platens. If reground platens sell for $ 8.0 each, how man must be reground and sold to break even? A) C() = ; 18 platens B) C() = ; 7 platens C) C() = ; 11 platens D) C() = ; 11 platens 13) Northwest Molded molds plastic handles which cost $0.90 per handle to mold. The fied cost to run the molding machine is $4680 per week. If the compan sells the handles for $3.90 each, how man handles must be molded and sold weekl to break even? A) 160 handles B) 40 handles C) 00 handles D) 97 handles 14) A lumber ard has fied costs of $ per da and variable costs of $0.04 per board-foot produced. Lumber sells for $1.44 per board-foot. How man board-feet must be produced and sold dail to break even? A) 94 board-feet B) 19 board-feet C) 80,90 board-feet D) 170 board-feet Page

23 . Building Linear Functions from Data; Direct Variation 1 Draw and Interpret Scatter Diagrams MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Plot a scatter diagram. 1) A) B) C) D) Page 3

24 ) A) B) C) D) Plot and interpret the appropriate scatter diagram. 3) The table gives the times spent watching TV and the grades of several students. Weekl TV (h) Grade (%) Which scatter diagram describes the data and the relationship, if an? Page 4

25 A) More hours spent watching TV ma reduce grades. B) More hours spent watching TV ma increase grades. C) More hours spent watching TV ma reduce grades. D) none of these Page

26 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 4) The table shows the stud times and test scores for a number of students. Draw a scatter plot of score versus time treating time as the independent variable. Stud Time (min) Test Score ) The one-da temperatures for 1 world cities along with their latitudes are shown in the table below. Make a scatter diagram for the data. Describe what happens to the one -da temperatures as the latitude increases. Cit Temperature (F) Latitude Oslo, Norwa Seattle, WA Anchorage, AK Paris, France Vancouver, Canada London, England Toko, Japan Cairo, Egpt Meico Cit, Meico Miami, FL New Delhi, India Manila, Philippines Latitude (degrees) Temperature (F) Page 6

27 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 6) The following scatter diagram shows heights (in inches) of children and their ages. Height (inches) Age (ears) What happens to height as age increases? A) Height increases as age increases. B) Height decreases as age increases. C) Height stas the same as age increases. D) Height and age do not appear to be related. 7) The following scatter diagram shows heights (in inches) of children and their ages. Height (inches) Age (ears) What is the epected height range for a -ear old child? A) -38 inches B) 0-30 inches C) 40-0 inches D) 3-4 inches Page 7

28 8) The following scatter diagram shows heights (in inches) of children and their ages. Height (inches) Age (ears) Based on this data, how old do ou think a child is who is about 39 inches tall? A) 3 ears B) 3 months C) 1 ear D) 7 ears Distinguish between Linear and Nonlinear Relations MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine if the tpe of relation is linear, nonlinear, or none. 1) A) linear B) nonlinear C) none Page 8

29 ) A) linear B) nonlinear C) none 3) A) nonlinear B) linear C) none 4) A) nonlinear B) linear C) none Page 9

30 ) A) nonlinear B) linear C) none 6) A) none B) linear C) nonlinear Page 30

31 Solve the problem. 7) Identif the scatter diagram of the relation that appears linear. A) B) C) D) 3 Use a Graphing Utilit to Find the Line of Best Fit MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a graphing utilit to find the equation of the line of best fit. Round to two decimal places, if necessar. 1) A) = 3 B) = C) =.8 D) = ) 3) A) = B) = C) = D) = A) = B) = C) = D) = Page 31

32 4) A) = B) = C) = D) = ) 6) 7) 8) 9) ) A) = B) = C) = D) = A) = B) = C) = D) = A) = B) = C) = D) = A) = B) = - 3 C) = D) = A) = B) = 4 C) = D) = A) = B) = - 8 C) = 0. - D) = ) A) = B) = C) = D) = ) A) = B) = C) = D) = Page 3

33 13) Ten students in a graduate program were randoml selected. Their grade point averages (GPAs) when the entered the program were between 3. and 4.0. The following data were obtained regarding their GPAs on entering the program versus their current GPAs. Entering GPA Current GPA A) = B) = C) = D) = ) Two different tests are designed to measure emploee productivit and deterit. Several emploees are randoml selected and tested with these results. Productivit Deterit A) = B) = C) = D) = ) Managers rate emploees according to job performance and attitude. The results for several randoml selected emploees are given below. Performance Attitude A) = B) = C) = D) = Page 33

34 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 16) The one-da temperatures for 1 world cities along with their latitudes are shown in the table below. Make a scatter diagram for the data. Then find the line of best fit and graph it on the scatter diagram. Cit Temperature (F) Latitude Oslo, Norwa Seattle, WA Anchorage, AK Paris, France Vancouver, Canada London, England Toko, Japan Cairo, Egpt Meico Cit, Meico Miami, FL New Delhi, India Manila, Philippines Latitude (degrees) Temperature (F) Page 34

35 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 17) A drug compan establishes that the most effective dose of a new drug relates to bod weight as shown below. Let bod weight be the independent variable and drug dosage be the dependent variable. Use a graphing utilit to draw a scatter diagram and to find the line of best fit. What is the most effective dosage for a person weighing 10 lbs? Bod Drug Weight (lbs) Dosage (mg) A) 14.0 mg B) 7.1 mg C) 1 mg D) mg 18) A marina owner wishes to estimate a linear function that relates boat length in feet and its draft (depth of boat below water line) in feet. He collects the following data. Let boat length represent the independent variable and draft represent the dependent variable. Use a graphing utilit to draw a scatter diagram and to find the line of best fit. What is the draft for a boat 60 ft in length (to the nearest tenth)? Boat Length (ft) Draft (ft) A) 9.7 B) 1.7 C). D).3 19) A surve of the interest rates earned b Certificates of Deposit (CDs) showed the following percents for the length of time (in ears) for holding the CD. Let length of time represent the independent variable and interest rate represent the dependent variable. Use a graphing utilit to draw a scatter diagram and to find the line of best fit. What is the estimate of the interest rate for a CD held for 30 ears (to the nearest thousandth)? CD Maturit (rs) Interest rate (%) A) B) 8.67 C) D) Page 3

36 0) Super Sall, a trul amazing individual, picks up a rock and throws it as hard as she can. The table below displas the relationship between the rockʹs horizontal distance, d (in feet) from Sall and the initial speed with which she throws. Initial speed( in ft/sec), v Horizontal distance of the rock (in feet), d Assume that the horizontal distance travelled varies linearl with the speed with which the rock is thrown. Using a graphing utilit, find the line of best fit, and estimate, rounded to two decimal places, the horizontal distance of the rock if the initial speed is 33 ft/sec. A) feet B) 6.67 feet C) feet D) feet SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) The following data represents the amount of mone Tom is saving each month since he graduated from college. month savings $ $70 $81 $91 $ $118 $13 Using the line of best fit for the data set, predict the amount he will save in the 4th month after graduating from college. ) The following data represents the amount of mone Tom is saving each month since he graduated from college. month savings $ $70 $81 $91 $ $118 $13 Find the slope of the line of best fit for the data set and interpret it. 3) The following data represents the Olmpic winning time in Womenʹs 0 m Freestle. ear time Using the line of best fit (with slope correct to decimal places) for the data set, predict the Olmpic winning time in ) The following data represents the Olmpic winning time in Womenʹs 0 m Freestle. ear time Find the slope of the line of best fit for the data set and interpret it. ) The following data represents the number of emploees at a compan at the start of each ear since the compan began. month number Using the line of best fit for the data set, predict the number of emploees at the start of the th ear. Page 36

37 6) The following data represents the number of emploees at a compan at the start of each ear since the compan began. month number Find the slope of the line of best fit for the data set and interpret it. 4 Construct a Linear Model Using Direct Variation MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. If varies directl as, find a linear function which relates them. 1) = 4 when = 0 A) f() = B) f() = C) f() = + 16 D) f() = 4 ) = 3 when = 36 A) f() = 8 9 B) f() = 9 C) f() = - 4 D) f() = 4 8 3) = 7 when = 1 9 A) f() = 63 B) f() = 63 C) f() = D) f() = 7 4) = 0.6 when = 0.3 A) f() = B) f() = 0.3 C) f() = D) f() = 0. ) = 0.7 when =.8 A) f() = 0. B) f() = 0.7 C) f() = -.1 D) f() = 4 Solve. 6) The amount of water used to take a shower is directl proportional to the amount of time that the shower is in use. A shower lasting 1 minutes requires 16.8 gallons of water. Find the amount of water used in a shower lasting 7 minutes. A).6 gallons B) 147 gallons C) 4.8 gallons D) 6.4 gallons 7) If the resistance in an electrical circuit is held constant, the amount of current flowing through the circuit varies directl with the amount of voltage applied to the circuit. When 11 volts are applied to a circuit, 7 milliamperes of current flow through the circuit. Find the new current if the voltage is increased to 13 volts. A) 3 milliamperes B) 143 milliamperes C) 31 milliamperes D) 30 milliamperes 8) The amount of gas that a helicopter uses is directl proportional to the number of hours spent fling. The helicopter flies for hours and uses gallons of fuel. Find the number of gallons of fuel that the helicopter uses to fl for 3 hours. A) 33 gallons B) 6 gallons C) 36 gallons D) 44 gallons Page 37

38 .3 Quadratic Functions and Their Zeros 1 Find the Zeros of a Quadratic Function b Factoring MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use factoring to find the zeros of the quadratic function. List the -intercepts of the graph of the function. 1) f() = A) = -11, = 8 B) = 11, = 8 C) = -11, = 1 D) = 11, = -8 ) g() = A) = 4, = 6 B) = -4, = -6 C) = -4, = 6 D) = 4, = 0 3) F() = A) = -3, = 4 B) = 3, = 4 C) = 1, = 1 D) = -3, = -4 4) h() = A) = -, = 8 B) =, = 8 C) = -, = 1 D) =, = -8 ) f() = A) = 11, = -6 B) = 11, = 6 C) = -11, = 1 D) = -11, = 6 6) G() = - A) = 0, = B) = 0, = - C) = D) = - 7) f() = A) = 9 4, = -1 B) = 4 9, = -1 C) = 4 9, = 1 D) = 4 9, = 0 8) g() = - 1 A) = 1, = - 1 B) = 1 C) = - 1 D) = 1, = 0 9) F() = A) = 3, = - 3 B) = 3, = 3 C) = - 3, = - 3 D) =- 3, = 3 ) h() = - 4 A) = 0, = B) = C) =, = D) = 0 11) f() = - 9 A) = -3, = 3 B) = -81, = 81 C) = 3 D) = -3 Page 38

39 Find the Zeros of a Quadratic Function Using the Square Root Method MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the zeros of the quadratic function using the Square Root Method. List the -intercepts of the graph of the function. 1) f() = - 9 A) = -3, = 3 B) = -81, = 81 C) = 3 D) = -3 ) F() = - A) =, = - B) = -, = C) = D) = 3) g() = ( - 3) - 49 A) = -4, = B) = C) = -7, = 7 D) = -, = -4 4) h() = ( + ) - 4 A) = -7, = - 3 B) = - 3 C) = -, = D) = -7 ) G() = ( - ) - 9 A) = 1, = 4 B) = -4, = -1 C) =, = 8 D) = -8, =- 3 Find the Zeros of a Quadratic Function b Completing the Square MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the zeros of the quadratic function b completing the square. List the -intercepts of the graph of the function. 1) f() = A) = 4, = -8 B) = -4, = 8 C) = 6, = -1 D) = -4, = -8 ) g() = A) =, = -1 B) = 1, = -1 C) = 1, = 1 D) = 1, = 0 3) F() = A) = 8, = 6 B) = -8, = -6 C) = 48, = -48 D) = 4, = 6 4) f() = A) = - 3 7, = 1 7 B) = 3 7, = 1 7 C) = 3 7, = - 7 D) = - 3 7, = - 7 ) g() = A) = -, = - 8 B) = -, = - 8 C) =, = 8 D) = - 8, = 4 6) f() = A) = -, = - 8 B) = -, = - 8 C) =, = 8 D) = - 8, = 4 Page 39

40 4 Find the Zeros of a Quadratic Function Using the Quadratic Formula MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the real zeros, if an, of each quadratic function using the quadratic formula. List the -intercepts, if an, of the graph of the function. 1) f() = A) = - 3, = B) = 3, = - C) = -3, = D) = - 3, = ) g() = A) = 9 ± 141 C) = B) = 9, = 1 D) No real zeros or -intercepts 3) G() = A) = -9, = B) = 9, = C) = 9, = - D) = -9, = - 4) H() = A) = - 1 4, = 8 B) = -4, = 8 C) = - 1 8, = 4 D) = - 1 8, = -4 ) F() = A) = 7 ± 69 C) = -7 ± 69 B) = D) No real zeros or -intercepts 6) h() = A) = -, = 4 B) = 4, = -8 C) = 6, = - D) No real zeros or -intercepts Find the Point of Intersection of Two Functions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve f() = g(). Find the points of intersection of the graphs of the two functions. 1) f() = 4 + g() = A) = -1, = B) = 1, = C) = -1, = 1 D) = 1, = - 1 Page 40

41 ) f() = g() = A) = 3, = -3 B) = 1 3, = -3 C) = - 18, = 18 D) = -, = 3) f() = 13 g() = -4 A) = , = 0 B) = ± 4 13 C) = 0 D) = 4 13, = 0 4) f() = g() = 31 A) = -7, = 0 B) = 0, = 7 C) = 7 ± 31 D) no real numbers 6 Solve Equations That Are Quadratic in Form MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the real zeros of the function. List the -intercepts of the graph of the function. 1) f() = 4-81 A) = -3, = 3 B) = -9, = 9 C) = - 3, = 3 D) no real solution ) F() = A) = -1, = 1, = -6, = 6 B) = -6, = 6 C) = -36, = 36 D) = -37, = 37 3) G() = A) = -6, = 6 B) = - 3, = 3 C) = -36, = 3 D) no real solution 4) h() = A) = -, = B) = - 1 3, = 1 3, = -, = C) = D) no real solution ) H() = A) = 4, = -1 B) = 64 C) = 4 D) = -4, = 1 6) f() = ( + 1) + 7( + 1) + A) = - 7, = - B) =, = 0 C) = -, = - D) = - 7 4, = -1 Page 41

42 7) P() = ( - 6) - 4( - 6) + 3 A) = 9, = 7 B) = - 9, = - 7 C) = 3, = - D) = - 3 6, = 8) Q() = (-7 + 1) - (-7 + 1) - 8 A) = 3 7, = B) = - 3 7, = 3 7 C) = -, = 4 D) = 1 7, = - 7 Solve the problem. 9) The length of a vegetable garden is 3 feet longer than its width. If the area of the garden is 70 square feet, find its dimensions. A) 7 ft b ft B) 6 ft b 11 ft C) 8 ft b 11 ft D) 6 ft b 9 ft ) An open bo is to be constructed from a square sheet of plastic b removing a square of side inches from each corner, and then turning up the sides. If the bo must have a volume of 4 cubic inches, find the length of one side of the open bo. A) 11 in. B) 13 in. C) 1 in. D) in. 11) A ball is thrown verticall upward from the top of a building 18 feet tall with an initial velocit of 11 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s = t - 16t. After how man seconds will the ball pass the top of the building on its wa down? A) 7 sec B) 18 sec C) 6 sec D) 9 sec 1) As part of a phsics eperiment, Ming drops a baseball from the top of a 3-foot building. To the nearest tenth of a second, for how man seconds will the baseball fall? (Hint: Use the formula h = 16t, which gives the distance h, in feet, that a free-falling object travels in t seconds.) A) 4. sec B) 81.3 sec C) 0.3 sec D) 1.1 sec 13) If a polgon, of n sides has 1 n(n - 3) diagonals, how man sides will a polgon with 434 diagonals have? A) 31 sides B) 3 sides C) 30 sides D) 33 sides Page 4

43 .4 Properties of Quadratic Functions 1 Graph a Quadratic Function Using Transformations MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the graph to one of the listed functions. 1) - - A) f() = + B) f() = - C) f() = D) f() = ) A) f() = B) f() = - 6 C) f() = D) f() = - 6 Page 43

44 3) A) f() = B) f() = - 4 C) f() = D) f() = - 4 4) A) f() = + 4 B) f() = + 4 C) f() = D) f() = Graph the function f b starting with the graph of = and using transformations (shifting, compressing, stretching, and/or reflection). ) f() = Page 44

45 A) B) C) D) ) f() = Page 4

46 A) B) C) D) ) f() = Page 46

47 A) B) C) D) ) f() = Page 47

48 A) B) C) D) Page 48

49 9) f() = A) B) C) D) Page 49

50 ) f() = A) B) C) D) ) f() = Page 0

51 A) B) C) D) ) f() = Page 1

52 A) B) C) D) ) f() = Page

53 A) B) C) D) ) f() = Page 3

54 A) B) C) D) ) f() = Page 4

55 A) B) C) D) Identif the Verte and Ais of Smmetr of a Quadratic Function MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the verte and ais of smmetr of the graph of the function. 1) f() = + A) (-, -); = - B) (-, ); = - C) (, -); = D) (, -); = ) f() = - 8 A) (4, -16); = 4 B) (-16, 4); = -16 C) (-4, 16); = -4 D) (16, -4); = 16 3) f() = A) (3, 9); = 3 B) (-9, 3); = -9 C) (-3, -9); = -3 D) (9, -3); = 9 4) f() = A) (-3, 9); = -3 B) (-9, 3); = -9 C) (3, -9); = 3 D) (9, -3); = 9 ) f() = A) (-3, 7); = -3 B) (3, 7); = 3 C) (-3, 0); = -3 D) (3, 0); = 3 6) f() = A) (-, -9); = - B) (, -9); = C) (, 9); = D) (-, 9); = - Page

56 7) f() = A) (1, 8) ; = 1 B) (-1, 4) ; = -1 C) (, 7) ; = D) (-1, 6) ; = -1 8) f() = A) (-1, -4) ; = -1 B) (1, 4) ; = 1 C) (-, ) ; = - D) (, 14) ; = 9) f() = A) - 11, ; = - 11 B) 11, 39 4 ; = 11 C) (-9, 8) ; = -9 D) (11, 0) ; = 11 ) f() = A) - 1 6, ; = C) 1 6, 41 6 ; = 1 6 B) (6, -7); = 6 D) -6, ; = -6 Page 6

57 3 Graph a Quadratic Function Using Its Verte, Ais and Intercepts MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the function using its verte, ais of smmetr, and intercepts. 1) f() = A) verte (, -4) intercepts (0, 0), (4, 0) B) verte (-, -4) intercepts (0, 0), (-4, 0) C) verte (-, 4) intercept (0, 8) D) verte (, 4) intercept (0, 8) Page 7

58 ) f() = A) verte (-4, 16) intercepts (0, 0), (-8, 0) 40 B) verte (-4, -16) intercept (0, -3) C) verte (4, 16) intercepts (0, 0), (8, 0) 40 D) verte (4, -16) intercept (0, -3) Page 8

59 3) f() = A) verte (-1, 0) intercepts (0, 1), (-1, 0) B) verte (1, 0) intercepts (0, 1), (1, 0) C) verte (1, 1) intercept (0, ) D) verte (-1, 1) intercept (0, ) Page 9

60 4) f() = A) verte (-1, -4) intercepts (1, 0), (- 3, 0), (0, -3) B) verte (1, -4) intercepts (-1, 0), (3, 0), (0, -3) C) verte (1, 4) intercepts (-1, 0), (3, 0), (0, 3) D) verte (-1, 4) intercepts (1, 0), (- 3, 0), (0, 3) Page 60

61 ) f() = A) verte (-3, 4) intercepts (-1, 0), (-, 0), (0, -) B) verte (3, -4) intercepts (1, 0), (, 0), (0, ) C) verte (3, 4) intercepts (1, 0), (, 0), (0, -) D) verte (-3, -4) intercepts (-1, 0), (-, 0), (0, ) Page 61

62 6) f() = A) verte (, -1) intercepts (3, 0), (1, 0), (0, 3) B) verte (-, -1) intercepts (-3, 0), (- 1, 0), (0, 3) C) verte (-, 1) intercepts (-3, 0), (- 1, 0), (0, -3) D) verte (, 1) intercepts (3, 0), (1, 0), (0, -3) Page 6

63 7) f() = A) verte (3, 4) intercepts (, 0), (1, 0), (0, -) B) verte (-3, -4) intercepts (-, 0), (- 1, 0), (0, ) C) verte (-3, 4) intercepts (-, 0), (- 1, 0), (0, -) D) verte (3, -4) intercepts (, 0), (1, 0), (0, ) Page 63

64 8) f() = A) verte (-, 3) intercept (0, 3) B) verte (, 3) intercept (0, 3) C) verte (-, 3) intercept 0, 31 D) verte (, 3) intercept 0, Page 64

65 9) f() = A) verte , intercept (0, -1) 0 1 B) verte , intercept (0, 1) C) verte 1 11, D) verte 1 11, intercept (0, -1) intercept (0, 1) Page 6

66 Determine the domain and the range of the function. ) f() = + 1 A) domain: all real numbers range: { -36} C) domain: { 6} range: { 36} B) domain: { -6} range: { -36} D) domain: all real numbers range: { 36} 11) f() = A) domain: all real numbers range: { 36} C) domain: { 6} range: { 36} B) domain: { -6} range: { 36} D) domain: all real numbers range: { -36} 1) f() = A) domain: all real numbers range: { 0} C) domain: { -1} range: { 0} B) domain: { 1} range: { 0} D) domain: all real numbers range: { 1} 13) f() = A) domain: all real numbers range: { -9} C) domain: range: { 4} range: { 9} B) domain: range: { 4} range: { -9} D) domain: all real numbers range: { 9} 14) f() = A) domain: all real numbers range: { 4} C) domain: { -1} range: { -4} B) domain: { -1} range: { 4} D) domain: all real numbers range: { -4} 1) f() = A) domain: all real numbers range: { -9} C) domain: all real numbers range: { 9} B) domain: { -4} range: { -9} D) domain: all real numbers range: all real numbers 16) f() = A) domain: all real numbers range: { 1} C) domain: all real numbers range: { -1} B) domain: { -} range: { 1} D) domain: all real numbers range: all real numbers Page 66

67 17) f() = A) domain: all real numbers range: C) domain: all real numbers range: 0 7 B) domain: all real numbers range: D) domain: all real numbers range: 0 7 Determine where the function is increasing and where it is decreasing. 18) f() = - 4 A) increasing on (, ) decreasing on (-, ) C) increasing on (-, -) decreasing on (-, ) B) increasing on (-, ) decreasing on (, ) D) increasing on (-, ) decreasing on (-, -) 19) f() = - - A) increasing on (-, -1) decreasing on (-1, ) C) increasing on (1, ) decreasing on (-, 1) B) increasing on (-1, ) decreasing on (-, -1) D) increasing on (-, 1) decreasing on (1, ) 0) f() = A) increasing on (3, ) decreasing on (-, 3) C) increasing on (-, -3) decreasing on (-3, ) B) increasing on (-, 3) decreasing on (3, ) D) increasing on (-3, ) decreasing on (-, -3) 1) f() = A) increasing on (-1, ) decreasing on (-, -1) C) increasing on (-9, ) decreasing on (-, -9) B) increasing on (-, -1) decreasing on (-1, ) D) increasing on (-, -9) decreasing on (-9, ) ) f() = A) increasing on (-, -1) decreasing on (-1, ) C) increasing on (-, 4) decreasing on (4, ) B) increasing on (-1, ) decreasing on (-, -1) D) increasing on (4, ) decreasing on (-, 4) 3) f() = A) increasing on (, ) decreasing on (-, ) C) increasing on (-, -9) decreasing on (-9, ) B) increasing on (-, ) decreasing on (, ) D) increasing on (-9, ) decreasing on (-, -9) Page 67

68 4) f() = A) increasing on (-, ) decreasing on (, ) C) increasing on (1, ) decreasing on (-, 1) B) increasing on (, ) decreasing on (-, ) D) increasing on (-, 1) decreasing on (1, ) ) g() = A) decreasing on (-, -1) increasing on (-1, ) C) decreasing on (-, 1) increasing on (1, ) B) increasing on (-, -60) decreasing on (-60, ) D) increasing on (-, -1) decreasing on (-1, ) 6) f() = A) increasing on -, - 1 decreasing on - 1, C) increasing on -, 1 decreasing on 1, B) decreasing on -, - 1 increasing on - 1, D) increasing on -, - 4 decreasing on - 4, Determine the quadratic function whose graph is given. 7) Verte: (- 1, 4) -intercept: (0, 3) A) f() = B) f() = C) f() = D) f() = Page 68

69 8) (0, 1) - (-, -3) - A) f() = B) f() = C) f() = D) f() = Find the Maimum or Minimum Value of a Quadratic Function MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine, without graphing, whether the given quadratic function has a maimum value or a minimum value and then find that value. 1) f() = + 4 A) minimum; 4 B) minimum; 0 C) maimum; 0 D) maimum; 4 ) f() = - 8 A) minimum; -8 B) minimum; 0 C) maimum; -8 D) maimum; 0 3) f() = A) minimum; - B) maimum; - C) minimum; 1 D) maimum; 1 4) f() = A) maimum; B) minimum; C) minimum; - 1 D) maimum; - 1 ) f() = A) minimum; B) maimum; C) minimum; 1 4 D) maimum; 1 4 6) f() = 3-9 A) minimum; B) maimum; C) minimum; 3 D) maimum; 3 7) f() = - - A) maimum; B) minimum; C) minimum; - D) maimum; - 8) f() = A) maimum; B) minimum; C) maimum; 7 7 D) minimum; 7 7 Page 69

70 Solve the problem. 9) The manufacturer of a CD plaer has found that the revenue R (in dollars) is R(p) = -p p, when the unit price is p dollars. If the manufacturer sets the price p to maimize revenue, what is the maimum revenue to the nearest whole dollar? A) $70,80 B) $141,6 C) $83,0 D) $66,440 ) The owner of a video store has determined that the cost C, in dollars, of operating the store is approimatel given b C() = , where is the number of videos rented dail. Find the lowest cost to the nearest dollar. A) $700 B) $0 C) $60 D) $800 11) The price p and the quantit sold of a certain product obe the demand equation p = , What quantit maimizes revenue? What is the maimum revenue? A) 0; $1,00 B) 1; $937 C) 37; $937 D) 00; $1,00 1) The price p and the quantit sold of a certain product obe the demand equation p = , What price should the compan charge to maimize revenue? A) $90 B) $8 C) $13 D) $4 13) The price p (in dollars) and the quantit sold of a certain product obe the demand equation = -7p + 4, 0 p 3. What quantit maimizes revenue? What is the maimum revenue? A) 11; $179 B) 6; $1344 C) 168; $1344 D) 4; $179 14) The price p (in dollars) and the quantit sold of a certain product obe the demand equation p = , 0 8. What price should the compan charge to maimize revenue? A) $14 B) $16.8 C) $1 D) $7 1) The profit that the vendor makes per da b selling pretzels is given b the function P() = Find the number of pretzels that must be sold to maimize profit. A) 300 pretzels B) 600 pretzels C) 0.6 pretzels D) 30 pretzels 16) The owner of a video store has determined that the profits P of the store are approimatel given b P() = , where is the number of videos rented dail. Find the maimum profit to the nearest dollar. A) $1666 B) $1600 C) $366 D) $300 17) You have 176 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maimize the enclosed area. A) 44 ft b 44 ft B) 88 ft b 88 ft C) 88 ft b ft D) 46 ft b 4 ft Page 70

71 18) A developer wants to enclose a rectangular grass lot that borders a cit street for parking. If the developer has 84 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? A),08 ft B) 0,164 ft C) 041 ft D) 1,13 ft 19) You have 7 feet of fencing to enclose a rectangular region. What is the maimum area? A) 464 square feet B) 18,496 square feet C) 73,984 square feet D) 460 square feet 0) You have 116 feet of fencing to enclose a rectangular plot that borders on a river. If ou do not fence the side along the river, find the length and width of the plot that will maimize the area. A) length: 8 feet, width: 9 feet B) length: 87 feet, width: 9 feet C) length: 8 feet, width: 8 feet D) length: 9 feet, width: 9 feet 1) A projectile is fired from a cliff 600 feet above the water at an inclination of 4 to the horizontal, with a muzzle velocit of 90 feet per second. The height h of the projectile above the water is given b h() = -3 (90) , where is the horizontal distance of the projectile from the base of the cliff. Find the maimum height of the projectile. A) ft B) 16.6 ft C) 63.8 ft D) ft ) A projectile is fired from a cliff 00 feet above the water at an inclination of 4 to the horizontal, with a muzzle velocit of 380 feet per second. The height h of the projectile above the water is given b h() = -3 (380) , where is the horizontal distance of the projectile from the base of the cliff. How far from the base of the cliff is the height of the projectile a maimum? A) 6. ft B) ft C) ft D) ft 3) Consider the quadratic model h(t) = -16t + 40t + 0 for the height (in feet), h, of an object t seconds after the object has been projected straight up into the air. Find the maimum height attained b the object. How much time does it take to fall back to the ground? Assume that it takes the same time for going up and coming down. A) maimum height = 7 ft; time to reach ground =. seconds B) maimum height = 7 ft; time to reach ground = 1. seconds C) maimum height = 0 ft; time to reach ground = 1. seconds D) maimum height = 0 ft; time to reach ground =. seconds 4) An object is propelled verticall upward from the top of a 11-foot building. The quadratic function s(t) = -16t + 176t + 11 models the ballʹs height above the ground, s(t), in feet, t seconds after it was thrown. How man seconds does it take until the object finall hits the ground? Round to the nearest tenth of a second if necessar. A) 11.6 seconds B) 0.6 seconds C). seconds D) seconds Page 71

72 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. ) A suspension bridge has twin towers that are 1300 feet apart. Each tower etends 180 feet above the road surface. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cable at a point 00 feet from the center of the bridge. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 6) Alan is building a garden shaped like a rectangle with a semicircle attached to one short side. If he has 0 feet of fencing to go around it, what dimensions will give him the maimum area in the garden? A) width = 0 π , length = 7 B) width = 0 7, length = 14 π + 4 C) width = 0 0 9, length = 13. D) width = 14, length = 18 π + 8 π + 4 7) The quadratic function f() = models the median, or average, age,, at which U.S. men were first married ears after In which ear was this average age at a minimum? (Round to the nearest ear.) What was the average age at first marriage for that ear? (Round to the nearest tenth.) A) 19, 3.7 ears old B) 19, 48.4 ears old C) 1936, 48.4 ears old D) 19, 36 ears old. Inequalities Involving Quadratic Functions 1 Solve Inequalities Involving Quadratic Functions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the inequalit. 1) A) [-1, 4] B) (-, -1] C) [4, ) D) (-, -1] or [4, ) ) > 0 A) (-, -) or (1, ) B) (-, 1) C) (-, -) D) (1, ) 3) A) (-, 0] or [6, ) B) [0, 6] C) (-, -6] or [0, ) D) [-6, 0] 4) A) (-, -7] or [0, ) B) [0, 7] C) (-, 0] or [7, ) D) [-7, 0] ) + 0 A) [-, 0] B) [0, ] C) (-, -] or [0, ) D) (-, 0] or [, ) 6) - 0 A) [0, ] B) [-, 0] C) (-, -] or [0, ) D) (-, 0] or [, ) Page 7

73 7) - 81 > 0 A) (-, -9) or (9, ) B) (-9, 9) C) (-, -81) or (81, ) D) (-81, 81) 8) A) [-3, 3] B) (-, -3] or [3, ) C) (-, -9] or [9, ) D) [-9, 9] 9) + -6 A) (-, -3] or [-, ) B) [-3, -] C) (-, -3] D) [-, ) ) - 8 < -18 A) - 4, B), 4 C) - 4, - D) -, 4 11) < 6 A) -, 7 4 B) 7 4, C) -, D) - 7 4, 1) 40( - 1) > 39 A) -, - 8 or 8, B) - 8, 8 C) -, - 8 or 8, D) - 8, 8 Solve the problem. 13) If f() = 6 - and g() = + 3, solve for f() = g() A) = 3, = B) = 1 3, = - 3 C) = 1 6, = 1 D) = - 1, = 1 14) If f() = 6 - and g() = + 3, solve f() g(). A) - 1 3, 3 B) - 3, 1 3 C) - 1 3, 3 D) - 1 3, 3 1) If g() = and h() = 19, then solve g() > h(). A) -, - 9 or 9, B) - 9, 9 C) -, - 9 or 9, D) - 9, 9 16) If h() = , solve h() > 0. A) (-, -3) or (-1, ) B) (-3, -1) C) (-, -3) D) (-1, ) 17) If g() = - - 6, solve g() 0. A) [-1, 6] B) (-, -1] C) [6, ) D) (-, -1] or [6, ) Page 73

74 18) The revenue achieved b selling graphing calculators is figured to be (48-0.) dollars. The cost of each calculator is $40. How man graphing calculators must be sold to make a profit (revenue - cost) of at least $63.80? A) { 11 < < 9} B) { 1 < < 19} C) { 1 < < } D) { 13 < < 7} 19) A rock falls from a tower that is 336 ft high. As it is falling, its height is given b the formula h = t. How man seconds will it take for the rock to hit the ground (h =0)? A) 4.6 s B) 18.3 s C) 706 s D) 17.9 s 0) A rock falls from a tower that is 17.4 m high. As it is falling, its height is given b the formula h = t. How man seconds will it take for the rock to hit the ground (h =0)? A).1 s B) 11.3 s C) 3300 s D) 11.1 s 1) A flare fired from the bottom of a gorge is visible onl when the flare is above the rim. If it is fired with an initial velocit of 160 ft/sec, and the gorge is 336 ft deep, during what interval can the flare be seen? (h = -16t + vot + ho.) A) 3 < t < 7 B) 6 < t < C) 0 < t < 3 D) 9 < t < 13 ) A coin is tossed upward from a balcon 188 ft high with an initial velocit of 3 ft/sec. During what interval of time will the coin be at a height of at least 60 ft? (h = -16t + vot + ho.) A) 0 t 4 B) 0 t 1 C) 4 t 8 D) 3 t 4 3) If a rocket is propelled upward from ground level, its height in meters after t seconds is given b h = -9.8t + 98t. During what interval of time will the rocket be higher than 0.8 m? A) 3 < t < 7 B) 0 < t < 3 C) 7 < t < 6 D) 6 < t < 4) A flare fired from the bottom of a gorge is visible onl when the flare is above the rim. If it is fired with an initial velocit of 160 ft/sec, and the gorge is 336 ft deep, during what interval can the flare be seen? (h = -16t + vot + ho.) A) 3 < t < 7 B) 6 < t < C) 0 < t < 3 D) 9 < t < 13 ) A coin is tossed upward from a balcon 4 ft high with an initial velocit of 16 ft/sec. During what interval of time will the coin be at a height of at least 0 ft? (h = -16t + vot + ho.) A) 0 t 4 B) 0 t 1 C) 4 t 8 D) 3 t 4 6) If a rocket is propelled upward from ground level, its height in meters after t seconds is given b h = -9.8t + 7.8t. During what interval of time will the rocket be higher than 94 m? A) < t < 6 B) 0 < t < C) 6 < t < D) < t < 11 Page 74

75 .6 Quadratic Models 1 Solve Applied Problems b Building Quadratic Functions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) A projectile is thrown upward so that its distance above the ground after t seconds is h = -1t + 40t. After how man seconds does it reach its maimum height? A) 14 s B) 7 s C) 1s D) 8 s ) Alan is building a garden shaped like a rectangle with a semicircle attached to one short side. If he has 30 feet of fencing to go around it, what dimensions will give him the maimum area in the garden? 60 A) width = π , length = 4. B) width = 30 4., length = 8.4 π + 4 C) width = 60 π + 8.4, length = 8.1 D) width = , length =.8 π + 4 3) The number of mosquitoes M(), in millions, in a certain area depends on the June rainfall, in inches: M() = What rainfall produces the maimum number of mosquitoes? A) 9. in. B) 0 in. C) 361 in. D) 19 in. 4) The manufacturer of a CD plaer has found that the revenue R (in dollars) is R(p) = -p + 160p, when the unit price is p dollars. If the manufacturer sets the price p to maimize revenue, what is the maimum revenue to the nearest whole dollar? A) $11,680 B) $43,360 C) $486,70 D) $973,440 ) A projectile is thrown upward so that its distance above the ground after t seconds is h = -13t + 44t. After how man seconds does it reach its maimum height? A) 17 s B) 8 s C). s D) 34 s 6) The owner of a video store has determined that the cost C, in dollars, of operating the store is approimatel given b C() = , where is the number of videos rented dail. Find the lowest cost to the nearest dollar. A) $40 B) $300 C) $400 D) $0 7) A developer wants to enclose a rectangular grass lot that borders a cit street for parking. If the developer has 00 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? A) 000 ft B),000 ft C) 00 ft D) 700 ft 8) The quadratic function f() = models the median, or average, age,, at which U.S. men were first married ears after In which ear was this average age at a minimum? (Round to the nearest ear.) What was the average age at first marriage for that ear? (Round to the nearest tenth.) A) 190,.8 ears old B) 190, 46.3 ears old C) 1936, 46.3 ears old D) 191, 36 ears old Page 7

76 Use a Graphing Utilit to Find the Quadratic Function of Best Fit to Data MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a graphing calculator to plot the data and find the quadratic function of best fit. 1) Southern Granite and Marble sells granite and marble b the square ard. One of its granite patterns is price sensitive. If the price is too low, customers perceive that it has less qualit. If the price is too high, customers perceive that it is overpriced. The compan conducted a pricing test with potential customers. The following data was collected. Use a graphing calculator to plot the data. What is the quadratic function of best fit? Price, Buers, B $0 30 $30 0 $40 6 $60 7 $80 7 $0 0 $1 A) B() = B) B() = C) B() = D) B() = ) A rock is dropped from a tall building and its distance (in feet) below the point of release is recorded as accuratel as possible at various times after the moment of release. The results are shown in the table. Find the regression equation of the best model. (seconds after release) (distance in feet) A) = 1.9 B) = C) = ln D) = 13.0 e ) An engineer collects data showing the speed s of a given car model and its average miles per gallon M. Use a graphing calculator to plot the scatter diagram. What is the quadratic function of best fit? Speed, s mph, M A) M(s) = B) M(s) = C) M(s) = D) M(s) = Page 76