Section 6-1 Polynomial Functions. Polynomial Function  P(x) = 2x 3 – 5x 2 –2x+5  This is standard form. The exponent in a term determines the degree.

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Presentation transcript:

Section 6-1 Polynomial Functions

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.

Classification

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 –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.

Regressions  Linear Model  Y = mx+b

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

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

xy 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

To estimate the number of employees for 1988, you can use the Table function option of a graphing calculator to find that ƒ(13) According to the model, there were about 62 employees in The table shows data on the number of employees that a small company had from 1975 to Find a cubic function to model the data. Use it to estimate the number of employees in Let 0 represent To find a cubic model, use the CubicReg option of a graphing calculator. The function ƒ(x) = x 3 – 0.375x x is an approximate model for the cubic function Number of Employees Year Enter the data. Graph the model.

Checking for Understanding me the answers Write each polynomial in standard form. Then classify it by degree and by number of terms. 1.–x 2 + 2x + x x x 3