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Questions and Answers
Which type of function(s) will be modeled with technology? (Select all that apply)
Which type of function(s) will be modeled with technology? (Select all that apply)
- Quadratic (correct)
- Cubic (correct)
- Square root (correct)
- Absolute value
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.
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).
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?
What was Juan's initial investment if his investment account can be modeled by c(x) = 7x^2 - 6x + 5, in thousands of dollars?
Use technology to determine an appropriate model of the data: (0,1), (1,4), (2,5), (3,4), (4,1).
Use technology to determine an appropriate model of the data: (0,1), (1,4), (2,5), (3,4), (4,1).
Find the time when a free-falling object hits the ground using the function h(t) = - 12t^2 + 36t.
Find the time when a free-falling object hits the ground using the function h(t) = - 12t^2 + 36t.
Find the time when the soccer ball reaches its maximum height using h(t) = - 8t^2 + 32t.
Find the time when the soccer ball reaches its maximum height using h(t) = - 8t^2 + 32t.
Using the quadratic model h(x) = - 3x^2 + 18x + 7, what is the maximum height the football will reach?
Using the quadratic model h(x) = - 3x^2 + 18x + 7, what is the maximum height the football will reach?
Using the quadratic model h(x) = - 3x^2 + 18x + 7, at what time will the ball reach its maximum height?
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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