Quadratic Functions in Real-Life Scenarios
Explore the comparison of quadratic functions through practical applications such as modeling jumps from cliffs, designing amusement park rides, and analyzing cable heights of bridges. Learn to determine heights, lengths, and optimal paths using quadratic equations in a real-world context.
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Presentation Transcript
Comparing Characteristics of Quadratic Functions Essential Questions: How do you compare two quadratic functions? What are the four forms of a quadratic function?
Warm-Up 1. Jason and Jim jumped off of a cliff into the ocean in Acapulco while vacationing Jason s height as a function of time could be modeled by the function h(t) = -16t +16t + 480, while Jim s height could be modeled by h(t) = -16t2 + 12t + 480 where t is the time in seconds and h is the height in feet. Whose jump was higher and by how much? 2. Solve the quadratic function: x2 9 = 0
You are helping design an amusement park. You have decided where to place the swinging ship ride. However, you need to determine how much space the ride needs to take up while it is in motion. In order to do this we need to figure out how much horizontal space the ride will take when it is at its widest point. The equation represents the path of the swinging ship ride. How can we determine the space needed for the ride? x2 10x+ 30 Graph this quadratic. Make sure to include as many extrema points as possible.
Using Bridges to Compare Quadratic Functions Verrazano Bridge Brooklyn Bridge Tappan Zee bridge
Three surveyors are having a discussion about bridges in New York City. The first surveyor collected data from the Verrazano Bridge, he measured the height of the cable as he drove from one end to the other. The second surveyor took a picture of the cable for the Brooklyn Bridge. The last surveyor came up with an equation to model the cable height of the Tappan Zee bridge.
A. Using the information, determine the length of each bridge between the two towers to decide which one is longest and shortest. B. Which bridge s cable gets the closest to the road? How do you know this? C. Analyze the data to determine which bridge a trucker should use if their truck s height is 15 ft. How did you come to this conclusion? Which bridge should he avoid and why?
The baseball team has decided to have a throwing contest. Below is the data for 3 different players. A. Whose ball was in the air the longest? B. Who threw their ball the highest? C. If you were to determine the winner of the contest, who would you choose and why?
HW: Worksheet
