Back to Lesson 9-9-B REPRESENTATIONS Objective G. Let f() =. a. What are the coordinates of the verte? b. Is the verte a minimum or a maimum? c. Complete the table of values below. 3 0 3 f() d. Graph the equation. f(). Refer to the graph at the right. -5-3 f() 0 8 6 - - - -6-8 -0 3 5 a. Does the parabola open up or down? Copright Wright Group/McGraw-Hill b. What are the coordinates of the verte? c. Is the verte a minimum or a maimum? d. Use the graph to estimate the value of f(.5). e. Is ( 3, 0) a point of the graph? Eplain how ou know. Algebra 9
Back to Lesson 9-9-B page 3. The graph below has equation f() = 0.5. -0-8 -6 - - - f() 6 5 3-3 -5 6 8 0 a. Find if = 0. b. From the graph, estimate the value of if = 5. c. Find the values if =. d. From the graph, estimate the value(s) of for which =.5. e. What is the ais of smmetr for this function?. Consider the function f() = 5. a. Complete the table of values below. 5 0 5 0 5 0 5 f() b. Graph the equation. f() c. Use the graph to estimate the value(s) of when = 5.6. d. The point (, 78.) lies on this parabola. What are the coordinates of its reflection image over the -ais? Copright Wright Group/McGraw-Hill 0 Algebra
Back to Lesson 9-9-B SKILLS Objective A. Solve 3 = 7 b using a graph.. Solve 5 = 5 b graphing = 5 and = 5. -0-8 -6-30 7 8 5 9 6 3 6 8 0-5 -3 - - -5-0 -5-0 -5-30 -35 0 5-50 3 5 3. Let = + 5. Solve + 5 = 7 using the table. 5 3 0 3 35 7 3 7 3 5 3 7 3 7. Let f() = ( - ). Create a table of values to help ou solve ( - ) = 6. 3 0 3 f() In 5 0, solve the equation. Give the eact answer(s). 5. = 0 6. 6a = 7 7. b - 35 = 65 8. - 7c = 5 9. ( - 9) = 3 0. 3 5 (d + 3) = 5 Copright Wright Group/McGraw-Hill Algebra
Back to Lesson 9-9-B page USES Objectives D and E In, use the equation d = 6t where d = distance in feet, and t = time in seconds. Approimate the answer to the nearest thousandth of a second.. Emil drops a ball from a ledge in the loft of her home, which is 3 feet above the famil room floor. How long will it take the ball to hit the floor?. A book falls off the top of an 8-foot shelf. Theodore is feet tall. If it takes Theodore seconds to respond to the fall and get out of the wa, does the book hit him? Eplain. 8 ft ft 3. Cats are known to alwas land on their feet. A cat climbed to the top of a 30-foot tree. She lost her footing and fell to the ground. After how man seconds is she back on her feet?. Caitln bumped a ladder, which had a pail of paint sitting on it 6 feet from the ground. She is 5.5 feet tall. How man seconds does she have to react so the pail of paint doesn t land on her? Eplain. 6 ft 5.5 ft Copright Wright Group/McGraw-Hill 5. A 0-foot ladder is being used to clean windows that are 6 feet from the ground on Sean s house. How far from the base of the house should the ladder be placed so that the top of the ladder reaches the windows? 6. Cherl has two square gardens. The length of the larger garden is 5 more than twice the length of the smaller garden. The area of the larger garden is 96 square feet. a. What is the length of the smaller garden? b. What is the area of the smaller garden? Algebra 3
Back to Lesson 9-3 9-3A REPRESENTATIONS Objective H In, match the graph with its equation. A = 3 + B = 3 + C = 3 - D = 3 -.. 6 8-3 - - -8 - -6 3-3 6 8 - - -8 - -6 3 3.. 6 8-3 - - -8 - -6 3-3 6 8 - - -8 - -6 3 5. Let f() = + 3 + 0. a. Fill in the table. 5 3 0 3 5 f() b. Using the table, estimate the verte. c. Identif the -intercepts. Identif the -intercept. d. Find an equation of the ais of smmetr. 6. Graph = + 7-33 on our calculator. a. Give the dimensions of the window that allow ou to see the verte and -intercepts. b. Estimate the coordinates of the verte to the nearest tenth. c. Estimate the -intercepts to the nearest tenth. 7. True or False. Consider h() = - 5 +. a. The graph of h() opens down. Copright Wright Group/McGraw-Hill b. The verte is approimatel ( 0.6,.6). c. The graph has no -intercepts. Algebra
Back to Lesson 9 9A USES Objective D. Suppose the height h of a ball versus time t is given b the formula h(t) = 6t + 3t + 6. a. Is the height of the ball being measured in feet or meters? b. At what height was the ball released? c. What was the initial upward velocit of the ball?. Mourette is a member of her high school golf team. She hits a golf ball off the ground with an initial upward velocit of 60 meters per second. a. Write a formula describing the height h of the ball (in meters) after t seconds. b. After how man seconds, to the nearest tenth, will the golf ball land on the ground? c. What is the maimum height the golf ball reaches? 3. Suppose a soccer ball is kicked off of the ground with an initial upward velocit of 73 feet per second at the same time a baseball is released from a height of 5 feet 6 inches with an initial upward velocit of feet per second. a. Which ball will sta in the air longer? Justif our answer. b. Which ball will reach a higher point? Justif our answer. Copright Wright Group/McGraw-Hill. During Super Bowl XXXIII, Denver Bronco quarterback John Elwa threw an 80-ard pass (longest of his career) to Rod Smith. Suppose Elwa released the ball from a height of 6 feet 3 inches and that the maimum height the ball reached was 8 feet and this occurred 38 ards awa from Elwa. a. What is a third point that can be assumed on the path of the football from Elwa to Smith? b. Use the three points and quadratic regression to find a formula for the height of the football in feet based on the ards it is from Elwa. c. At about what height did Rod Smith catch the football? Algebra 7
Back to Lesson 9-5 9-5B SKILLS Objective B. If - 5 - = 0, complete the following. a. The equation is given in the form b. Solve the equation using the Quadratic a + b + c = 0. What are the values Formula. of a, b, and c? c. Fill in the table of values below. d. Graph the equation to check our solutions. 0 6. If 5 = + 5, complete the following. a. Rewrite the equation in the form b. Solve the equation using the Quadratic a + b + c = 0. What are the values Formula. of a, b, and c? c. Fill in the table of values below. d. Graph the equation to check our solutions. 3 5 6 Copright Wright Group/McGraw-Hill Algebra 3
Back to Lesson 9-5 9-5B page In 3 5, solve using the Quadratic Formula. Give eact answers. 3. - 6 + 6 = 0. r = r + 5. = 7 - In 6, solve using the Quadratic Formula. Round answers to the nearest hundredth. 6. 3a - 6 = 0 7. 5m - 0 = 7m 8. 5 = 6 + 7 9. n - n = 0. 6(h - h) = 7. - 5 = 0. In 5-meter platform diving, the function h(t) =.9t +.3t + 5 gives the approimate height h (in meters) above the water a diver is t seconds after launching the dive. How man seconds elapse from the time the diver leaves the 5-meter platform until the diver hits the water? 3. If a diver dives from a 5-foot platform with an initial velocit of 8 feet per second, the diver s approimate height in feet can be represented b the function h(t) = 6t + 8t + 5, where h is the height and t is the time in seconds. a. Find h(). Write a sentence eplaining what it means. b. Estimate the length of time the diver will be in the air before hitting the water. Copright Wright Group/McGraw-Hill 3 Algebra
Back to Lesson 9-6 9-6B SKILLS Objective B In, fi nd all real solutions to the equations using the Quadratic Formula. Round our answers to the nearest hundredth.. 5a - a + = 0. b + 5b + 3 = 0 3. 5-0c + c = 0. 7d - d = 3 5. e - 36 = e 6. 3f = f - 7. 6g + 8g = 5 8. h(3 - h) -.5 = 0 9. 3( j + 7) = 7j 0. 3k - 6 = k. m = (m - ). 3(n - 9) = n(n - 7) Copright Wright Group/McGraw-Hill 3 Algebra
Back to Lesson 9-6 9-6B page PROPERTIES Objective C In 3 6, a quadratic equation is given. a. Find the discriminant. b. Give the number of real solutions to the equation. 3. 3 + - 7 = 0 a. b.. p + 6p - 6 = 0 a. b. 5. r = r 5 + a. b. 6. 9s ( s - 3 ) = 6 a. b. 7. The discriminant of t + bt + 7 = 0 is 7. Find the value(s) of b. 8. The discriminant of the equation a + b + c = 0 is 0. How man -intercepts are on the graph of this equation? 9. The discriminant of the equation a + b + c = 0 is. What does this indicate about the graph of = a + b + c? Copright Wright Group/McGraw-Hill 0. An equation in the form = a + b + c is graphed. Tell whether the value of the discriminant is positive, negative, or zero. 5 3-5 -3 - - - - -3-5 3 5 Algebra 35