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Unit 4 Lesson 8: Graphing Polynomial Functions

Unit 4 Lesson 8: Graphing Polynomial Functions. Common Core State Standards. Lesson Goals. 3:. Graph a polynomial function. ESLRs: Becoming Competent Learners and Complex Thinkers. Review of Some Terms. zero of a function:. A number, k , is a zero of a function when x is

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Unit 4 Lesson 8: Graphing Polynomial Functions

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  1. Unit 4 Lesson 8:Graphing Polynomial Functions Common Core State Standards Lesson Goals 3: • Graph a polynomial function. ESLRs: Becoming Competent Learners and Complex Thinkers

  2. Review of Some Terms zero of a function: A number, k, is a zero of a function when x is replaced with k and the answer is zero. factor of a function: An expression, (x – k), is a factor of a function when the function is divided by (x – k), the remainder is zero. solution of a function: The number, k, that results from solving a function when the function is set equal to zero.

  3. Review of Some Terms If the number, k, is a real number, then k is also an x-intercept for the graph of the function. y x

  4. Graphing Polynomial Functions y Turning Points: The y-coordinate of a turning point is a local maximum if it is higher than nearby points or a local minimum if it is lower than nearby points. y is a local maximum. y is a local minimum. x A function with degree n has at most n – 1 turning points. If the function has n zeros, then the function has exactly n – 1 turning points

  5. Determine the lowest-degree polynomial that has the given graph. A function with degree n has at most n – 1 turning points. Is the degree even or odd? Is the leading coefficient positive or negative?

  6. Estimate the coordinates of each turning point. maximum minimum minimum Do the turning points correspond to a local minimum or a local maximum?

  7. What are the real zeros of the function.

  8. Determine the lowest-degree polynomial that has the given graph. A function with degree n has at most n – 1 turning points. Is the degree even or odd? Is the leading coefficient positive or negative?

  9. Estimate the coordinates of each turning point and state whether the turning point corresponds to a local minimum or a local maximum. maximum maximum minimum minimum

  10. What are the real zeros of the function.

  11. Graphing Polynomial Functions y degree: leading coefficient: x

  12. Graphing Polynomial Functions y zeros: x

  13. Graphing Polynomial Functions degree: leading coefficient: zeros: turning points:

  14. Graphing Polynomial Functions y x

  15. Graphing Polynomial Functions degree - shape leading coefficient - direction zeros – x-intercepts turning points U up no rational at most 3

  16. y x

  17. Today’s Assignment • p. 376: 15 – 27 l

  18. Check Assignment • p. 376: 15 – 27 l

  19. y Snake-shaped Rises left to right 3 real zeros 2 turning points x

  20. y Snake-shaped Rises left to right 1 real zero At most 2 turning points x

  21. maximum zeros minimum degree minimum

  22. zeros maximum maximum degree minimum

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