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Show that the following data can be modeled by a quadratic function. x 012 3 4 P(x) 6 8 12 18 26 Compute the first-order and second-order differences. P First-order difference Second-order difference Are second-order differences constant? Yes No 0 6 1 8 2 12 3 18 4 26

Show that the following data can be modeled by a quadratic function. x 012 3 4 P(x) 6 8 12 18 26 Compute the first-order and second-order differences. P First-order difference Second-order difference Are second-order differences constant? Yes No 0 6 1 8 2 12 3 18 4 26

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Show that the following data can be modeled by a quadratic function.

## Quadratic Function Analysis The goal is to determine if the following data can be modeled by a quadratic function. ### Data Table - **\( x \):** 0, 1, 2, 3, 4 - **\( P(x) \):** 6, 8, 12, 18, 26 ### Steps to Compute Differences 1. **First-order Differences:** - Calculate by subtracting each previous \( P(x) \) value from the current one. 2. **Second-order Differences:** - Calculate by subtracting each previous first-order difference from the current one. ### Table for Calculations | \( x \) | 0 | 1 | 2 | 3 | 4 | |-----------------------|----|----|----|----|----| | **\( P \)** | 6 | 8 | 12 | 18 | 26 | | **First-order difference** | | | | | | | **Second-order difference**| | | | | | ### Analysis After calculations, determine the consistency of the second-order differences. ### Question **Are second-order differences constant?** - ☐ Yes - ☐ No The constancy of second-order differences indicates that the data can be modeled by a quadratic function.
Transcribed Image Text:## Quadratic Function Analysis The goal is to determine if the following data can be modeled by a quadratic function. ### Data Table - **\( x \):** 0, 1, 2, 3, 4 - **\( P(x) \):** 6, 8, 12, 18, 26 ### Steps to Compute Differences 1. **First-order Differences:** - Calculate by subtracting each previous \( P(x) \) value from the current one. 2. **Second-order Differences:** - Calculate by subtracting each previous first-order difference from the current one. ### Table for Calculations | \( x \) | 0 | 1 | 2 | 3 | 4 | |-----------------------|----|----|----|----|----| | **\( P \)** | 6 | 8 | 12 | 18 | 26 | | **First-order difference** | | | | | | | **Second-order difference**| | | | | | ### Analysis After calculations, determine the consistency of the second-order differences. ### Question **Are second-order differences constant?** - ☐ Yes - ☐ No The constancy of second-order differences indicates that the data can be modeled by a quadratic function.
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