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Understanding Polynomial Functions and Their Properties

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This guide delves into polynomial functions, covering critical concepts like roots, discriminants, factored forms, and vertex forms. Explore the properties of quadratic functions, including finding roots through various methods such as the discriminant and graphing techniques. Learn the significance of the vertex in relation to the graph and the behavior of roots, particularly under different conditions. Ideal for students and enthusiasts eager to grasp the fundamentals of polynomial functions and their visual representations.

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Understanding Polynomial Functions and Their Properties

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  1. FUNCTIONS TABLES No calculators GRAPHS ROOTS FACTORED FORM 100 100 100 100 100 200 200 200 200 200 300 300 300 300 300 400 400 400 400 400 500 500 500 500 500

  2. FUNCTIONS $100 The roots of F(x)=x2+4x-12

  3. FUNCTIONS 200 The discriminant of F(x)=x2-4x+1

  4. FUNCTIONS 300 Factored form of F(x)=x2-4x+1

  5. FUNCTIONS 400 Graph of F(x)=-2x2+12x-18

  6. FUNCTIONS 500 Vertex Form of F(x)=-2x2+2x-5

  7. Kind of Function for

  8. Value of a

  9. Value of b

  10. Value of c

  11. Discriminant of

  12. Roots of

  13. Factored Form of

  14. Polynomial Form of

  15. Vertex Form of

  16. Value of Discriminant

  17. ROOTS 100 Value of discriminant if only root at x=3

  18. ROOTS 200 Positive, Negative or 0,discriminant if roots are x=(2+3i) and x=(2-3i)

  19. Graph if root is at x=3 and table :

  20. ROOTS 400 Vertex if roots are x=2+√3 , x=2-√3

  21. ROOTS 500 Graph if roots are x=2+√3 , x=2-√3

  22. FACTORED FORM 100 Polynomial Form of F(x)=(x+6)(x-2)

  23. Factored Form 200 Graph of f(x)=(x-(2-√(3))(x-(2+√(3))

  24. FACTORED FORM 300 Value of Discriminant of F(x)=(x+3)2

  25. FACTORED FORM 400 Vertex form of F(x)=(x-(.5+1.5i))(x-(.5-1.5i))

  26. FACTORED FORM 500 Vertex form of f(x)=(x-(2+i√(3)))(x-(2-i√(3)))

  27. FINAL JEOPARDY!

  28. Without using a calculator, the polynomial form using

  29. YEA!!!!!

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