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15 Name: Analyzing Graphs of Quadratic Functions 1. Use the graph at the right to fill in the blanks for each point. a) (, 24) represents Point. b) (12, ) represents Point. c) (, ) represents Point F. d) (, 32) represents Point. e) (, ) represents Point C. f) ( 6, ) represents Point. g) Point D represents the of the graph. h) This graph has one -intercept and two -intercepts. What s the Point? 2. For each point, use the graph to the right to determine the missing coordinate, then graph and label the point. a) (3, ) Label this point A. b) (, 1) & (, 1) Label these points B and C. c) (6, ) Label this point D. d) (, 0) Label this point E. This point represents the of the graph. e) (, 4) & (, 4) Label these points F and G. f) (4, ) Label this point H. g) On this graph we see x-intercept(s) and y-intercept(s).

16 Name: Analyzing Graphs of Quadratic Functions Launch! Three rockets are launched at the same time. Each person in the group chooses one rocket. Each graph shows the height of one rocket over time. Work with your group to answer these questions. 1. Which rocket returned to ground level first? 2. Which rocket reached the greatest height? What height did it reach? 3. How many seconds was your rocket in the air? Which rocket(s) was in the air for more than 2.5 seconds? 4. From what height was your rocket launched? Which rockets were at the same height at the same time? What was the height and time? 5. Which rocket(s) reached a height of at least 25 meters? 6. Which rocket was launched from a height of 10 meters? Launch! Three rockets are launched at the same time. Each person in the group chooses one rocket. Each graph shows the height of one rocket over time. Work with your group to answer these questions. 1. Which rocket returned to ground level first? 2. Which rocket reached the greatest height? What height did it reach? 3. How many seconds was your rocket in the air? Which rocket(s) was in the air for more than 2.5 seconds? 4. From what height was your rocket launched? Which rockets were at the same height at the same time? What was the height and time? 5. Which rocket(s) reached a height of at least 25 meters? 6. Which rocket was launched from a height of 10 meters? Launch! Three rockets are launched at the same time. Each person in the group chooses one rocket. Each graph shows the height of one rocket over time. Work with your group to answer these questions. 1. Which rocket returned to ground level first? 2. Which rocket reached the greatest height? What height did it reach? 3. How many seconds was your rocket in the air? Which rocket(s) was in the air for more than 2.5 seconds? 4. From what height was your rocket launched? Which rockets were at the same height at the same time? What was the height and time? 5. Which rocket(s) reached a height of at least 25 meters? 6. Which rocket was launched from a height of 10 meters?

17 Name: Analyzing Graphs of Quadratic Functions Rocket Graph (1) Height (meters) Time (seconds)

18 Name: Analyzing Graphs of Quadratic Functions Rocket Graph (2) Height (meters) Time (seconds)

19 Name: Analyzing Graphs of Quadratic Functions Rocket Graph (3) Height (meters) Time (seconds)

20 Name: The Way the Ball Bounces Analyzing Graphs of Quadratic Functions Martin, Nathan, and Pamela are throwing tennis balls that were hit out of the court back to the players. For fun, all three decide to throw a ball at the same time. The graphs represent the height of each tennis ball versus time. Describe what the graph communicates. Attach the four statement cards that best describe the throw represented in the graph.

21 Name: Analyzing Graphs of Quadratic Functions The Way the Ball Bounces Martin, Nathan, and Pamela are throwing tennis balls that were hit out of the court back to the players. For fun, all three decide to throw a ball at the same time. The graphs represent the height of each tennis ball versus time. Describe what the graph communicates. Attach the four statement cards that best describe the throw represented in the graph.

22 Name: The Way the Ball Bounces Analyzing Graphs of Quadratic Functions Martin, Nathan, and Pamela are throwing tennis balls that were hit out of the court back to the players. For fun, all three decide to throw a ball at the same time. The graphs represent the height of each tennis ball versus time. Describe what the graph communicates. Attach the four statement cards that best describe the throw represented in the graph.

23 Analyzing Graphs of Quadratic Functions The Way the Ball Bounces: Statement Cards Cut apart each statement on the dotted lines. Place each card in the column that best describes the throw represented in the graph. Two sets of cards have been provided. Between 0.5 seconds and 0.75 seconds, the tennis ball descended 1 foot. At 0.25 second and 0.75 second, the tennis ball is seven feet above the ground. The tennis ball reaches its maximum height 0.5 second after being thrown. The tennis ball reached a maximum height of 13 feet. Of the three tennis balls, it took the longest time to land. The tennis ball was thrown from a height of six feet. Between 0.5 seconds and 0.75 seconds, the tennis ball descended 2 feet. The tennis ball was above 4 feet for about 1.5 seconds. The tennis ball was above 4 feet for about 1 second. Of the three tennis balls, it took the shortest amount of time to reach its maximum. The tennis ball reached the same height from which it was thrown when 0.75 seconds had passed. Between 0.5 seconds and 0.75 seconds, the tennis ball ascended 1 foot. Between 0.5 seconds and 0.75 seconds, the tennis ball descended 1 foot. At 0.25 second and 0.75 second, the tennis ball is seven feet above the ground. The tennis ball reaches its maximum height 0.5 second after being thrown. The tennis ball reached a maximum height of 13 feet. Of the three tennis balls, it took the longest time to land. The tennis ball was thrown from a height of six feet. Between 0.5 seconds and 0.75 seconds, the tennis ball descended 2 feet. The tennis ball was above 4 feet for about 1.5 seconds. The tennis ball was above 4 feet for about 1 second. Of the three tennis balls, it took the shortest amount of time to reach its maximum. The tennis ball reached the same height from which it was thrown when 0.75 seconds had passed. Between 0.5 seconds and 0.75 seconds, the tennis ball ascended 1 foot.

24 Name: Analyzing Graphs of Quadratic Functions Analyzing Graphs of Quadratic Functions Folded Notes Cut along the dotted lines. Fold along the solid lines. Answer the question(s) on the inside of each flap. On the outside of the flaps write Analyzing Graphs of Quadratic Functions. Tape in your notebook. Identify the independent and dependent variables. How are the two variables related? A rancher has 100 meters of fencing with which to build a rectangular corral. The graph below shows the relationship between the area and the length of the corral. Analyze the scales on the axes. What values are being used for each variable? Area (square meters) Does the graph have a maximum point or a minimum point? How does this vertex relate to the scenario? Identify the x- and y-intercepts. How do they relate to the scenario?

25 Name: Roller Coaster Ride Analyzing Graphs of Quadratic Functions A roller coaster at XTRA Fun Rides goes into an underground tunnel during the first descent of the ride. The coaster enters the tunnel three seconds after the first descent starts and stays in the tunnel for a total of 2 seconds. The roller coaster is 40 feet above ground one second after the initial drop. The graph below represents the height of the roller coaster versus the time passed since the initial drop. Use this information to label the graph, including the following: a title labels for the x and y-axes indicate the scale for each axis identify the x-intercepts, y-intercept, and vertex Use the graph to complete the table below. Attribute Coordinates of the point(s) Describe the point(s) on the graph Meaning of the point(s) in context y-intercept x-intercept(s) vertex

26 Name: Roller Coaster Ride* Analyzing Graphs of Quadratic Functions A roller coaster at XTRA Fun Rides goes into an underground tunnel during the first descent of the ride. The coaster enters the tunnel three seconds after the first descent starts and stays in the tunnel for a total of 2 seconds. The roller coaster is 40 feet above ground one second after the initial drop. The graph below represents the height of the roller coaster versus the time passed since the initial drop. Use this information to label the graph, including the following: a title labels for the x and y-axes indicate the scale for each axis identify the x-intercepts, y-intercept, and vertex Use the graph to complete the table below. Attribute Coordinates of the point(s) Describe the point(s) on the graph Meaning of the point(s) in context y-intercept (0, ) Where the graph crosses the The y-intercept is the height of the roller coaster at x-intercept(s) (, 0) & (, 0) Where the graph crosses the The x-intercept is when the roller coaster vertex (, )

27 Name: Analyzing Graphs of Quadratic Functions Evaluate: Analyzing Graphs of Quadratic Functions 1. The graph below represents the height of a rocket that is launched from the top of a building. Height of Rocket (feet) Time (seconds) Which statement best describes the path of the rocket? A The rocket reached the ground between 2.25 seconds and 2.5 seconds. B C The rocket was below 34 feet between 0.25 seconds and 1 second. The rocket reached its maximum between 1 second and 1.25 seconds. D The rocket descended 8 feet between 1.5 seconds and 1.75 seconds.

28 2. State the vertex of the graph below. Analyzing Graphs of Quadratic Functions A B C D 2 2 1, , , , 1 3 3

29 3. Which statement best describes the graph below? Analyzing Graphs of Quadratic Functions Height (feet) Time (seconds) A The ball was dropped from a height of 18 feet and then reached a maximum height of 20 feet before reaching the ground. B C The ball was thrown from the ground and then reached a height of 18 feet before landing again in just under 2 seconds. The ball was dropped from a height of 18 feet and then descended for just under 2 seconds before it hit the ground. D The ball was thrown from a height of 2 feet and then descended for 18 seconds before hitting the ground.

30 4. The graph below shows the height of a ball versus time for one bounce. Analyzing Graphs of Quadratic Functions Height (feet) Time (seconds) For how many seconds was the ball at a height of 7 feet or more above the ground? A 0.25 seconds B C 1 seconds 1.5 seconds D 1.75 seconds