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4.9 Modeling with Polynomial Functions with answers
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4.9 Modeling with Polynomial Functions
ACT Practice:What are the possible values of y such that xy2 = 54, x < 10, y < 10, and x and y are integers?
F. 3, 3
G. 1, 3
H. 1, 9
J. 3
K. 6
4.9 Modeling with Polynomial Functions with answers
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Writing Polynomial Functions for a Set of Points
Use factors and another point to find a (your vertical stretch/compression)
4.9 Modeling with Polynomial Functions with answers
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Example: Write a cubic function that passes through the given points.
(4, 0), (0, 10), (2, 0), (5, 0)
(1, 0), (0, 12), (2, 0), (3, 0)
Practice: Write a cubic function that passes through the given points.
4.9 Modeling with Polynomial Functions with answers
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Finite Differences of Polynomials
Function Type Degree Constant Finite Difference
* Linear 1 * First
Quadratic * 2 * Second
* Cubic * 3 Third
*Quartic 4 * Fourth
*Quintic 5 * Fifth
4.9 Modeling with Polynomial Functions with answers
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EXAMPLE 1: Use finite differences to determine the degree of the polynomial that best describes the data.
4.9 Modeling with Polynomial Functions with answers
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The table shows the closing value of a stock index on the first day of trading for various years.
• To create a mathematical model for the data, you will need to determine what type of function is most appropriate.• Finite difference is a method that can be used to identify the degree of any polynomial data.• Then use the regression tool on your calculator to write the polynomial function. • Careful to choose the right type based on your finite differences!!!
4.9 Modeling with Polynomial Functions with answers
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EXAMPLE 2: Write a polynomial function for the data.
Step 1: Finite Differences
Step 2: Use the regression in your calculator to help you write the function.
x 1 2 3 4 5 6 7
f(x) 20 4 0 4 16 40 84
4.9 Modeling with Polynomial Functions with answers
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EXAMPLE 3: The data in the table shows the wave height (in inches) over a 7second period. Write a polynomial model and then estimate using your model.
STEPS:
1) differences
2) calculator regression
3) Is your model reasonable for the next 7second interval?
seconds 1 2 3 4 5 6 7
height (in) 0.5 3 6.5 12 20.5 33 50.5
4.9 Modeling with Polynomial Functions with answers
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HW: Pg. 223: 3, 5, 7, 9, 13, 23, 25 32
