Evaluating and Graphing Polynomial Functions

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Presentation transcript:

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:

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

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

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

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.

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

Evaluating and Graphing Polynomial Functions Example 2a Use synthetic substitution to evaluate the polynomial functions for the value of x. 3 4 −10 −3 5 −2 + 12 6 9 42 × 4 2 3 14 40

Evaluating and Graphing Polynomial Functions Example 2b Use synthetic substitution to evaluate the polynomial functions for the value of x. 2 −2 0 3 −5 7 −9 −4 −8 −10 −30 −46 −2 −4 −5 −15 −23 −55

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 −5 6 −2 −7 2 −3 10 −32 68 −122 240 −5 16 −34 61 −120 237 p