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Warm Up: Solve & Sketch the graph:

Warm Up: Solve & Sketch the graph:. Real Zeros of Polynomial Functions. Objective. Long Division of Polynomials Short Division of Polynomials Write the Polynomial when given the zeros. Relevance. Learn how to evaluate data from real world applications that fit into a quadratic model.

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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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