Examples of different polynomial graphs

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Examples of different polynomial graphs

  1. 1. Polynomial Functions and Models
  2. 2. Turning Points and Local Extrema <ul><li>Turning point </li></ul><ul><ul><li>A point (x, y) on the graph </li></ul></ul><ul><ul><li>Located where graph changes </li></ul></ul><ul><ul><ul><li>from increasing </li></ul></ul></ul><ul><ul><ul><li>to decreasing </li></ul></ul></ul><ul><ul><ul><li>(or vice versa) </li></ul></ul></ul>• •
  3. 3. Family of Polynomials <ul><li>Constant polynomial functions </li></ul><ul><ul><li>f(x) = a </li></ul></ul><ul><li>Linear polynomial functions </li></ul><ul><ul><li>f(x) = m x + b </li></ul></ul><ul><li>Quadratic polynomial functions </li></ul><ul><ul><li>f(x) = a x 2 + b x + c </li></ul></ul>
  4. 4. Family of Polynomials <ul><li>Cubic polynomial functions </li></ul><ul><ul><li>f(x) = a x 3 + b x 2 + c x + d </li></ul></ul><ul><ul><li>Degree 3 polynomial </li></ul></ul><ul><li>Quartic polynomial functions </li></ul><ul><ul><li>f(x) = a x 4 + b x 3 + c x 2 + d x + e </li></ul></ul><ul><ul><li>Degree 4 polynomial </li></ul></ul>
  5. 5. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x 4 + 4x 3 – 2x – 1 Quartic Function Degree = 4 Max. Zeros: 4
  6. 6. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x 5 + 4x 4 – 2x 3 – 4x 2 + x – 1 Quintic Function Degree = 5 Max. Zeros: 5
  7. 7. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x 3 + 4x 2 + 2 Cubic Function Degree = 3 Max. Zeros: 3
  8. 8. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x 2 + 3x + 2 Quadratic Function Degree = 2 Max. Zeros: 2
  9. 9. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x + 2 Linear Function Degree = 1 Max. Zeros: 1
  10. 10. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = 3 Constant Function Degree = 0 Max. Zeros: 0

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