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X y -2 14 -1 -1 I 0 -6 1 -1 2 14 3 39 Finding first differences: -1-14--15, -6+1=-5, -1+6=5, 14+1-15, 39-14-25. Finding second differences: -5+15=10, 5+5=10, 15-5=10, 25-15=10. Since there is a constant in second differences, this is a quadratic equation..

X y -2 14 -1 -1 I 0 -6 1 -1 2 14 3 39 Finding first differences: -1-14--15, -6+1=-5, -1+6=5, 14+1-15, 39-14-25. Finding second differences: -5+15=10, 5+5=10, 15-5=10, 25-15=10. Since there is a constant in second differences, this is a quadratic equation..

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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### Data Table and Analysis **Table:** | x | y | |----|----| | -2 | 14 | | -1 | -1 | | 0 | -6 | | 1 | -1 | | 2 | 14 | | 3 | 39 | **Analysis:** **Finding First Differences:** - \(-1 - 14 = -15\) - \(-6 - (-1) = -5\) - \(-1 - (-6) = 5\) - \(14 - (-1) = 15\) - \(39 - 14 = 25\) **Finding Second Differences:** - \(-5 - (-15) = 10\) - \(5 - (-5) = 10\) - \(15 - 5 = 10\) - \(25 - 15 = 10\) Since there is a constant in the second differences, this indicates that the relationship can be modeled by a quadratic equation.
Transcribed Image Text:### Data Table and Analysis **Table:** | x | y | |----|----| | -2 | 14 | | -1 | -1 | | 0 | -6 | | 1 | -1 | | 2 | 14 | | 3 | 39 | **Analysis:** **Finding First Differences:** - \(-1 - 14 = -15\) - \(-6 - (-1) = -5\) - \(-1 - (-6) = 5\) - \(14 - (-1) = 15\) - \(39 - 14 = 25\) **Finding Second Differences:** - \(-5 - (-15) = 10\) - \(5 - (-5) = 10\) - \(15 - 5 = 10\) - \(25 - 15 = 10\) Since there is a constant in the second differences, this indicates that the relationship can be modeled by a quadratic equation.
- When the second differences are the **same**, it's a quadratic equation. Second differences are equal to 2a. To find "a," divide the second differences by 2. General equation is f(x) = ax² + bx + c; c is the y-intercept. \[ f(x) = ax^2 + bx + c \]
Transcribed Image Text:- When the second differences are the **same**, it's a quadratic equation. Second differences are equal to 2a. To find "a," divide the second differences by 2. General equation is f(x) = ax² + bx + c; c is the y-intercept. \[ f(x) = ax^2 + bx + c \]
Expert Solution
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The y-intercept is the point where the curve intersects the y axis. It is calculated by substituting x=0 in the function: y=f(x).

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