Questions and Answers
Which type of function(s) will be modeled with technology? (Select all that apply)
Given the table of data, determine the function that would most appropriately model the data: x 1 2 3 4, f(x) 4 3 4 7.
quadratic
Use technology to determine an appropriate model of the data: (-1,0), (1,-4), (2,-3), (4,5), (5,12).
f(x) = (x-1)^2 - 4
What was Juan's initial investment if his investment account can be modeled by c(x) = 7x^2 - 6x + 5, in thousands of dollars?
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Use technology to determine an appropriate model of the data: (0,1), (1,4), (2,5), (3,4), (4,1).
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Find the time when a free-falling object hits the ground using the function h(t) = - 12t^2 + 36t.
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Find the time when the soccer ball reaches its maximum height using h(t) = - 8t^2 + 32t.
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Using the quadratic model h(x) = - 3x^2 + 18x + 7, what is the maximum height the football will reach?
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Using the quadratic model h(x) = - 3x^2 + 18x + 7, at what time will the ball reach its maximum height?
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Study Notes
Modeling Functions Overview
- Functions that can be modeled with technology include cubic, absolute value, quadratic, and square root functions.
Quadratic Function Applications
- A dataset with values (1, 4), (2, 3), (3, 4), (4, 7) can be best modeled by a quadratic function.
- A specific function derived from the dataset of points (-1, 0), (1, -4), (2, -3), (4, 5), (5, 12) is f(x) = (x-1)² - 4.
Investment Model
- Juan’s investment account modeled by c(x) = 7x² - 6x + 5 indicates his initial investment was $5,000.
Data Modeling Examples
- The point dataset (0, 1), (1, 4), (2, 5), (3, 4), (4, 1) is approximated by the model f(x) = - (x-2)² + 5.
Free Falling Objects
- The height of a free-falling object can be computed using h(t) = -12t² + 36t, with the object hitting the ground at 3 seconds.
Soccer Ball Trajectory
- The soccer ball modeled by h(t) = -8t² + 32t reaches its maximum height at 2 seconds.
Maximum Height Calculation for Football
- For a football kicked, the function h(x) = -3x² + 18x + 7 indicates the maximum height the ball will reach is 34 feet.
- This football reaches its maximum height after 3 seconds.
Key Time Points
- Time to ground impact for the free falling object is 3 seconds.
- Maximum height of the soccer ball occurs at 2 seconds, and the football’s peak is also at 3 seconds.
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Description
This quiz covers key concepts related to modeling various types of functions using technology. It includes questions on cubic, quadratic, absolute value, and square root functions. Utilize the provided data points to determine the most appropriate function models.
