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Warm Up: Solve & Sketch the graph:

Learn to solve and sketch graphs of polynomial functions, find real zeros, use long and short division, and write polynomials from zeros. Understand the relevance in real-world applications and equivalent statements. Practice graph sketching based on multiplicity of zeros and finding polynomial functions from given zeros.

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Warm Up: Solve & Sketch the graph:

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  1. Warm Up: Solve & Sketch the graph:

  2. Real Zeros of Polynomial Functions

  3. Objective • Long Division of Polynomials • Short Division of Polynomials • Write the Polynomial when given the zeros.

  4. Relevance • Learn how to evaluate data from real world applications that fit into a quadratic model.

  5. Equivalent Statements: • x = a is a zero of the function f. • x = a is a solution of the polynomial equation f(x)=0. • (x-a) is a factor of the polynomial f(x) • (a, 0) is an x-intercept of the graph of f

  6. Multiplicity (Repeated Zeros)

  7. Sketch the graph: End behavior: Multiplicity of 2. Touches. Through these Points.

  8. Multiplicity - repeated zero – Means………….. • If it occurs an odd number of times, the graph crosses the x-axis at the zero. • If it occurs an even number of times, the graph will just touch the x-axis at the zero.

  9. Sketch the graph: 1st Term would be End Behavior: Mult. of 3 Goes Through Mult. Of 2 Touches x y 1 3

  10. Sketch the graph: 1st Term would be End Behavior: Both have a multiplicity of 2. Just Touch! x y -1 -1

  11. Can you write a polynomial function if you know the zeros?

  12. Find a Polynomial function that has the given zeros: 6, -3

  13. Find a Polynomial function that has the given zeros: 0, 3, -5

  14. Find a Polynomial function that has the given zeros: 3, 2, -2, -1

  15. Find a Polynomial function that has the given zeros: and

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