1. 6-1 Polynomial Functions

2. Objectives Exploring Polynomial Functions Modeling Data with a Polynomial Function

3. 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

4. Degrees of a Polynomial DegreeName Using Degree Polynomial ExampleNumber of Terms Name Using Number of Terms 0Constant61Monomial 1Linearx + 32Binomial 2Quadratic3x² 3Cubic2x³ - 5x² - 2x3Trinomial 4Quartic 5Quintic4 Polynomial of 4 Terms

5. Write each polynomial in standard form. Then classify it by degree and by number of terms. a.9 + x 3 b.x 3 – 2x 2 – 3x 4 x 3 + 9 –3x 4 + x 3 – 2x 2 The polynomial is a quartic trinomial. The term with the largest degree is x 3,so the polynomial is degree 3. It has two terms. The polynomial is a cubic binomial. The term with the largest degree is –3x 4, so the polynomial is degree 4. It has three terms. Classifying Polynomials

6. xy 02.8 25 46 65.5 84 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 modelQuadratic modelCubic model Comparing Models

7. 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) = 0.0096x 3 – 0.375x 2 + 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 of Employees Year Enter the data. Graph the model. Real World Connection