1. Section 6-1 Polynomial Functions

2. Polynomial Function  P(x) = 2x 3 – 5x 2 –2x+5  This is standard form. The exponent in a term determines the degree of that term.

3. Classification

4. 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.

5. Regressions  Linear Model  Y = mx+b

6. Regressions  Quadratic Model  Y = ax 2 +bx+c

7. Regressions  Cubic Model  y=ax 3 + bx 2 +cx+d

8. 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 model Cubic model

9. 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 1988. 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.

10. Checking for Understanding Email me the answers jmelfi@ocs.cnyric.org Write each polynomial in standard form. Then classify it by degree and by number of terms. 1.–x 2 + 2x + x 2 2. 7x 2 + 10 + 4x 3