1. Evaluating and Graphing Polynomial Functions
A polynomial function such as f(x) = 5x4 − 4x3 + 3x2 +2x + 1 has the following properties:
A coefficient is the number in front of a variable. The leading coefficient is in front of the variable with highest power.
Leading Coefficient: 5
Constant Term: 1
A Constant Term does not have a variable.
The degree is the highest power of a polynomial.
Degree: 4
The terms are written from the highest power to the lowest power.
Standard Form:
All powers are whole numbers. No decimals or fractions or negative powers are allowed in a polynomial power.
Exponents:

2. Evaluating and Graphing Polynomial Functions
f(x) = 2
f(x) = x + 1 y y x x
Constant
Function
Linear
Function
Degree = 0
Degree = 1
No Zeros
1 Zero

3. Evaluating and Graphing Polynomial Functions
f(x) = x2 + 2x − 3
f(x) = x3− 5x + 2 y y x x
Quadratic
Function
Cubic
Function
Degree = 2
Degree = 3
2 Zeros
3 Zeros

4. Evaluating and Graphing Polynomial Functions
f(x) = x4 − 3x3 + 2x2 +7x + 1
f(x) = x5− 5x3 + 4x y y x x
Quartic
Function
Quintic
Function
Degree = 4
Degree = 5
4 Zeros
5 Zeros

5. Evaluating and Graphing Polynomial Functions
Example 1
Determine if each expression is a polynomial function. If so, write it in standard form and state the degree.
Yes, the degree is 4.
Yes, the degree is 5.
No, contains fractional variable.
No, contains variable exponent.

6. Evaluating and Graphing Polynomial Functions
Example 1
Use direct substitution to evaluate the polynomial functions for the value of x.

7. Evaluating and Graphing Polynomial Functions
Example 2a
Use synthetic substitution to evaluate the polynomial functions for the value of x. 3
4 −10 − −2 + 12 6 9 42 × 4 2 3 14 40

8. Evaluating and Graphing Polynomial Functions
Example 2b
Use synthetic substitution to evaluate the polynomial functions for the value of x. 2
− − −9 −4 −8
−10
−30
−46 −2 −4 −5
−15
−23
−55

9. 6.2 Evaluating and Graphing Polynomial Functions, p. 329
Objective: To Evaluate and Graph Polynomial Functions; CA Std. 3.0
Example 2c
Use synthetic substitution to evaluate the polynomial functions for the value of x.
− 2
− −2 − −3 10
−32 68
−122
240 −5 16
−34 61
−120
237 p