Bellwork 5 81117 The following graph shows the

Bellwork #5 8/11/17 The following graph shows the velocity (in centimeters per second) and turbidity of the Logan River in Queensland, Australia during a flood Approximately when does the flood start?

Bellwork #6: 8/15/17 Simplify: 1) -7+5(2 -9) ) 6 2+4 -1 3) -13+15 -9(2)

Different Functions Linear uadratic xponential

Come up with tables of values that are linear exponential, quadratic, and none

Bellwork #7: 8/17/17 Draw a graph showing Kate's distance from her house over time: Kate walks for 10 minutes from her house to the grocery store. She spends 20 minutes shopping for groceries. She takes her bags and walks more slowly for 15 minutes back home.

Linear, quadratic, exponential, or none? x y -2 8 -1 5 0 4 1 5 2 8 3 13 x y -2 -1 0 1 2 3 1/8 1/2 2 8 x y 32 12 8 -2 -1 0 1 2 3 -24 -20 -16 -12 -8 -4 -2 -1 0 1 2 3 4 -4

Lesson 5: Two Graphing Stories Students interpret the meaning of the point of intersection of two graphs and use analytic tools to find its coordinates. Example 1 Consider the story: Maya and Earl live at opposite ends of the hallway in their apartment building. Their doors are 50 ft. apart. Each starts at his or her own door and walks at a steady pace toward each other and stops when they meet What would their graphing stories look like if we put them on the same graph? When the two people meet in the hallway, what would be happening on the graph? Sketch a graph that shows their distance from Maya’s door.

Exploratory Challenge/Exercises 1– 4 https: //www. youtube. com/watch? v=X 956 Evm. Cev. I&feature=youtu. be 1. Graph the man’s elevation on the stairway versus time in seconds. 2. Add the girl’s elevation to the same graph. How did you account for the fact that the two people did not start at the same time? 3. Suppose the two graphs intersect at the point P(24, 4). the meaning of this point in this situation? What is 4. Is it possible for two people, walking in stairwells, to produce the same graphs you have been using and not pass each other at time 12 sec. ? Explain your reasoning.

Example 2/Exercises 5– 7 Consider the story: Duke starts at the base of a ramp and walks up it at a constant rate. His elevation increases by 3 ft. every second. Just as Duke starts walking up the ramp, Shirley starts at the top of the same 25 ft. high ramp and begins walking down the ramp at a constant rate. Her elevation decreases 2 ft. every second. 5) Sketch two graphs on the same set of elevation-versus-time axes to represent Duke’s and Shirley’s motions. 6) What are the coordinates of the point of intersection of the two graphs? At what time do Duke and Shirley pass each other? 7) Write down the equation of the line that represents Duke’s motion as he moves up the ramp and the equation of the line that represents Shirley’s motion as she moves down the ramp. Show that the coordinates of the point you found in the question above satisfy both equations.

Lesson Summary The intersection point of the graphs of two equations is an ordered pair that is a solution to both equations. In the context of a distance (or elevation) story, this point represents the fact that both distances (or elevations) are equal at the given time. Graphing stories with quantities that change at a constant rate can be represented using piecewise linear equations.

Exit Ticket Refer back to the story in example 1. Suppose: Maya walks at a constant rate of 3 ft. every second. Earl walks at a constant rate of 4 ft. every second. 1) Graph both people’s distance from Maya’s door versus time in seconds 2) According to your graphs, approximately how far will they be from Maya’s door when they meet?

Bellwork #8: 8/18/17 Explain the differences between linear, exponential, and quadratic. *I will check the bellwork next week, so every two weeks **I will be checking homework, so make sure that is out

Tina and Miguel live at opposite ends of the hallway in their apartment building. Their doors are 27 ft. apart. Each starts at his or her own door and walks at a steady pace toward each other and stops when they meet. Tina is walking at a speed of 5 feet per second while Luis is walking at a speed of 4 feet per second. a. Sketch a graph of their distance from Maya’s door. b. How long will it take for them to meet?