The document discusses polynomial functions and their properties. It defines turning points as points where the graph of a function changes from increasing to decreasing. It then categorizes common polynomial functions as constant, linear, quadratic, cubic, or quartic depending on their degree. It provides examples of each type of polynomial function and notes that the maximum number of zeros is equal to the degree of the polynomial function.

1. Polynomial Functions and Models

2. Turning Points and Local Extrema Turning point A point (x, y) on the graph Located where graph changes from increasing to decreasing (or vice versa) • •

3. Family of Polynomials Constant polynomial functions f(x) = a Linear polynomial functions f(x) = m x + b Quadratic polynomial functions f(x) = a x 2 + b x + c

4. Family of Polynomials Cubic polynomial functions f(x) = a x 3 + b x 2 + c x + d Degree 3 polynomial Quartic polynomial functions f(x) = a x 4 + b x 3 + c x 2 + d x + e Degree 4 polynomial

5. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x 4 + 4x 3 – 2x – 1 Quartic Function Degree = 4 Max. Zeros: 4

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. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x 3 + 4x 2 + 2 Cubic Function Degree = 3 Max. Zeros: 3

8. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x 2 + 3x + 2 Quadratic Function Degree = 2 Max. Zeros: 2

9. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = x + 2 Linear Function Degree = 1 Max. Zeros: 1

10. POLYNOMIAL FUNCTIONS GENERAL SHAPES OF POLYNOMIAL FUNCTIONS f(x) = 3 Constant Function Degree = 0 Max. Zeros: 0