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Warm Up: Solve & Sketch the graph:

Warm Up: Solve & Sketch the graph:. Graphing Polynomials & Finding a Polynomial Function. 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.

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Warm Up: Solve & Sketch the graph:

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  1. Warm Up: Solve & Sketch the graph:

  2. Graphing Polynomials & Finding a Polynomial Function

  3. 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

  4. Multiplicity

  5. Repeated Zeros

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

  7. 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.

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

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

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

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

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

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

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

  15. Long & Synthetic Division

  16. Use Long Division and use the result to factor the polynomial completely. 1st Step:

  17. 2nd Step:

  18. Divide using long division: Remainder

  19. Divide using long division:

  20. You Try: Divide using long division

  21. Divide using long division

  22. Synthetic Division

  23. Divide using synthetic division to find the zeros:

  24. Divide using synthetic division:

  25. You Try: Divide using synthetic division – Find zeros: 4

  26. You Try: Divide using synthetic division:

  27. You Try: Divide using synthetic division:

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