6-1 Polynomial Functions. Objectives Exploring Polynomial Functions Modeling Data with a Polynomial...
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Transcript of 6-1 Polynomial Functions. Objectives Exploring Polynomial Functions Modeling Data with a Polynomial...
![Page 1: 6-1 Polynomial Functions. Objectives Exploring Polynomial Functions Modeling Data with a Polynomial Function.](https://reader036.fdocuments.net/reader036/viewer/2022071806/56649d095503460f949daf6d/html5/thumbnails/1.jpg)
6-1 Polynomial Functions
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Objectives
Exploring Polynomial Functions
Modeling Data with a Polynomial Function
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Vocabulary
A polynomial is a monomial or the sum of monomials.
The exponent of the variable in a term determines the degree of that term.
Ordering the terms by descending order by degree. This order demonstrates the standard form of a polynomial.
P(x) = 2x³ - 5x² - 2x + 5
Leading Coefficient
Cubic Term
Quadratic Term
Linear Term
Constant Term
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Degrees of a Polynomial
Degree Name Using Degree
Polynomial Example Number of Terms
Name Using Number of Terms
0 Constant 6 1 Monomial
1 Linear x + 3 2 Binomial
2 Quadratic 3x²
3 Cubic 2x³ - 5x² - 2x 3 Trinomial
4 Quartic
5 Quintic 4Polynomial of 4
Terms
234 53 xxx
153 235 xxx
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Write each polynomial in standard form. Then classify it by degree and by number of terms.
a. 9 + x3 b. x3 – 2x2 – 3x4
x3 + 9 –3x4 + x3 – 2x2
The polynomial is a quartic trinomial.
The term with the largest degree is x3,so the polynomial is degree 3.
It has two terms.The polynomial is a cubic binomial.
The term with the largest degree is –3x4, so the polynomial is degree 4. It has three terms.
Classifying Polynomials
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x y0 2.82 54 66 5.58 4
Using a graphing calculator, determine whether a linear,
quadratic, or cubic model best fits the values in the table.
Enter the data. Use the LinReg, QuadReg, and CubicReg options of a graphing calculator to find the best-fitting model for each polynomial classification.
Graph each model and compare.
The quadratic model appears to best fit the given values.
Linear model Quadratic model Cubic model
Comparing Models
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To estimate the number of employees for 1988, you can use the Table function option of a graphing calculator to find that ƒ(13) 62.72. According to the model, there were about 62 employees in 1988.
The table shows data on the number of employees that a small
company had from 1975 to 2000. Find a cubic function to model the data.
Use it to estimate the number of employees in 1998. Let 0 represent 1975.
To find a cubic model, use the CubicReg option of a graphing calculator.
The function ƒ(x) = 0.0096x3 – 0.375x2 + 3.541x + 58.96 is an approximate model for the cubic function.
1975 60
1980 65
1985 70
1990 60
1995 55
2000 64
Number ofEmployees
YearEnter the data.
Graph the model.
Real World Connection