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Polynomial Functions Day 1 and 2

Polynomial Functions Day 1 and 2. Polynomial Functions. Do now: Find the Range of yesterday’s exit ticket problem!. Exit Ticket: Start homework: Do not lose handout-hmwk #5. Objectives: Given a polynomial (many number) function, determine from the graph what degree is

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Polynomial Functions Day 1 and 2

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  1. Polynomial FunctionsDay 1 and 2

  2. Polynomial Functions • Do now: Find the Range of yesterday’s exit ticket problem! • Exit Ticket: Start homework: • Do not lose handout-hmwk #5 • Objectives:Given a polynomial (many number) function, determine from the graph what degree is • Find the “zeros” from the graph or the equation, in order to recognize equations of same degree

  3. Polynomial Functions (day 2) • Do now: Write the TWO fundamental Rules of Algebra you (memorized?!) • learned from yesterday’s powerpoint….! • Exit Ticket: • Sketch an exponential GROWTH function • Objectives:Given a polynomial (many number) function, determine from the graph what degree is • Find the “zeros” from the graph or the equation, in order to recognize equations of same degree

  4. Just a few definitions 

  5. Polynomial Functions The largest exponent within the polynomial determines the degree of the polynomial.

  6. Fundamental Theorem of Algebra: • Degree of the polynomial is the same as the number of “ups” and “downs” of its graph… • Try the examples in notes.

  7. Leading Coefficient The leading coefficient is the coefficient of the first term in a polynomial when the terms are written in descending order by degrees. For example, the cubic function f(x) = -2x3 + x2 – 5x – 10 has a leading coefficient of -2. This will play an important role in it’s graph…

  8. 2nd Fundamental Theorem of Algebra: The number of zeros that a polynomial function has is equal to that function’s degree.

  9. Explore Polynomials Linear Function Quadratic Function Cubic Function Quartic Function

  10. Graph A Graph B Cubic Polynomials Let’s look at the two graphs and let’s discuss the questions below. 1. How can you check to see if both graphs are functions? • 2. How many x-intercepts do graphs A & B have? 3. What is the end behaviour for each graph? 4. Which graph do you think has a positive leading coeffient? Why? 5. Which graph do you think has a negative leading coefficient? Why?

  11. Cubic Polynomials The following chart shows the properties of the graphs on the left.

  12. Cubic Polynomials The following chart shows the properties of the graphs on the left.

  13. Cubic Polynomials The following chart shows the properties of the graphs on the left.

  14. Graph A Graph B Quartic Polynomials Look at the two graphs and discuss the questions given below. 1. How can you check to see if both graphs are functions? • 2. How many x-intercepts do graphs A & B have? 3. What is the end behaviour for each graph? 4. Which graph do you think has a positive leading coeffient? Why? 5. Which graph do you think has a negative leading coefficient? Why?

  15. Quartic Polynomials The following chart shows the properties of the graphs on the left.

  16. Quartic Polynomials The following chart shows the properties of the graphs on the left.

  17. Quartic Polynomials The following chart shows the properties of the graphs on the left.

  18. Quartic Polynomials The following chart shows the properties of the graphs on the left.

  19. Polynomial Functions • Did we accomplish our objectives? • Any Questions? • Objectives:Given a polynomial (many number) function, determine from the graph what degree is • Find the “zeros” from the graph or the equation, in order to recognize equations of same degree

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