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Polynomial Functions Evaluation and Graphing

Learn about polynomial functions, their standard form, degree, leading coefficient, and end behavior. Practice evaluating and graphing polynomial functions.

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Polynomial Functions Evaluation and Graphing

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  1. Algebra II 5.2: Evaluate and Graph Polynomial Functions HW: p.341 (4-12 even, 16, 28, 30)

  2. Vocabulary Polynomial Function = a function in the form: where , exponents are whole numbers, coefficients are real, is the leading coefficient, and is the constant term. (whole numbers: 0, 1, 2, …) (real #’s: rational & irrational)

  3. Vocabulary Standard Form of a Polynomial = terms are written in descending order of exponents. Degree = the highest exponent.

  4. Common Polynomial Functions

  5. Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.

  6. Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.

  7. Direct vs. Synthetic Substitution. 1.) Evaluate the polynomial for the given value of x.

  8. Direct vs. Synthetic Substitution. 2.) Evaluate the polynomial for the given value of x.

  9. End Behaviors of a Polynomial Function • Degree: Odd • Leading Coefficient: Positive • Example: y = x3

  10. End Behaviors of a Polynomial Function • Degree: Odd • Leading Coefficient: Negative • Example: y = -x3

  11. End Behaviors of a Polynomial Function • Degree: Even • Leading Coefficient: Positive • Example: y = x2

  12. End Behaviors of a Polynomial Function • Degree: Even • Leading Coefficient: Negative • Example: y = -x2

  13. Given the degree and the leading coefficient, describe its end behavior and draw a possible sketch of the graph. 1.) degree: 4, leading coef.: -2 2.) degree: 7, leading coef.: 4

  14. Given the degree and the leading coefficient, describe its end behavior and draw a possible sketch of the graph. 3.) degree: 6, leading coef.: 1 4.) degree: 5, leading coef.: -6

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