5.2 Evaluate and Graph Polynomial Functions

Slides:

Advertisements

Similar presentations

7.1 An Introduction to Polynomials

Advertisements

A POLYNOMIAL is a monomial or a sum of monomials.

E VALUATING P OLYNOMIAL F UNCTIONS A polynomial function is a function of the form f (x) = a n x n + a n – 1 x n – 1 +· · ·+ a 1 x + a 0 Where a n  0.

“ARE YOU READY FOR THIS?”. 1. Classify this polynomial by degree: f(x) = 4x³ + 2x² - 3x + 7 a. binomial b. 4 term c. cubic d. quartic How do you know?

Warm Up #8 Evaluate the expression when x = –4 1. x2 + 5x

EXAMPLE 1 Identify polynomial functions 4 Decide whether the function is a polynomial function. If so, write it in standard form and state its degree,

Friday February 7, Properties of Exponent Objective: To evaluate or simplify expression with powers EQ: Can you multiply and divide negative fraction.

EXAMPLE 1 Identify polynomial functions

Evaluating and Graphing Polynomial Functions

5.2 Evaluating and Graphing Polynomial Functions DAY 1

Evaluate and Graph Polynomial Functions Section 2.2 How do you identify and evaluate polynomial functions? What is synthetic substitution? How do you graph.

6.2: E VALUATING AND GRAPHING POLYNOMIAL FUNCTIONS Objectives: Students will be able to identify, evaluate and graph a polynomial function.

POLYNOMIALS A polynomial is a sum or difference of monomials (terms). Two terms = binomial Three terms = trinomial E VALUATING P OLYNOMIAL F UNCTIONS.

 Students should be able to… › Evaluate a polynomial function. › Graph a polynomial function.

5-3: Polynomial Functions. A polynomial function is a function of the form f (x) = a n x n + a n – 1 x n – 1 +· · ·+ a 1 x + a 0 Where a n  0 and the.

7.1 Polynomial Functions Evaluate Polynomials

UNIT 2, LESSON 1 POLYNOMIAL FUNCTIONS. WHAT IS A POLYNOMIAL FUNCTION? Coefficients must be real numbers. Exponents must be whole numbers.

5.2 – Evaluate and Graph Polynomial Functions Recall that a monomial is a number, variable, or a product of numbers and variables. A polynomial is a monomial.

2.1 Evaluate and Graph Polynomial Functions Objectives: Identify, evaluate, add, and subtract polynomials Classify polynomials, and describe the shapes.

End behavior By:Skylar Brown.

1 Algebra 2: Section 6.2 Evaluating and Graphing Polynomial Functions (Day 1)

Standard form: terms are written in descending order of exponents from left to right. Leading Coefficient: the coefficient of the variable with the highest.

7.1 Polynomial Functions Objectives: 1.Evaluate polynomial functions. 2.Identify general shapes of graphs of polynomial function.

Advanced Algebra Notes Section 5.2: Evaluate and Graph Polynomial Functions A __________________ is a number, a variable, or the product of numbers and.

Questions from yesterday???.

Quadratic Functions 2A Polynomials. A polynomial in x is an expression that contains only non-negative, whole number powers of x. The degree of a polynomial.

Cubic Polynomial with degree: 3 QUARTIC Highest exponent is a 4 Polynomial of degree 4.

Evaluate the following functions with the given value.

Do Now: Match each polynomial function with its graph. Explain your reasoning. Use a graphing calculator to verify your answers. 1. f (x) = x 3 − x 2.

Algebra 2cc Section 2.10 Identify and evaluate polynomials A polynomial function is an expression in the form: f(x) = ax n + bx n-1 + cx n-2 + … dx + e.

Polynomial Function Review

Evaluating and Graphing Polynomial Functions

A polynomial is an expression that can be written in the form

2.1 Classifying Polynomials

6-3 Polynomials Warm Up Lesson Presentation Lesson Quiz

Let’s Begin!!! .

Algebra II Section 5-3 Polynomial Functions.

Pre-AP Algebra 2 Goal(s):

Evaluate and Graph Polynomial Functions

Algebra II with Trigonometry Ms. Lee

Objectives Classify polynomials and write polynomials in standard form. Evaluate polynomial expressions.

A POLYNOMIAL is a monomial or a sum of monomials.

Let’s Begin!!! .

n n – 1 f (x) = an x n + an – 1 x n – 1 +· · ·+ a 1 x + a 0 a 0 a0

Notes Over 6.2 Identifying Polynomial Functions Polynomial Function

Let’s Begin!!! .

6.2 Evaluating and Graphing Polynomials

Evaluate Polynomial Functions

Polynomial Functions and Models

Academy Algebra II 5.2: Evaluate and Graph Polynomial Functions

Solve the inequality and graph the solution set on the number line

Objectives Classify polynomials and write polynomials in standard form. Evaluate polynomial expressions.

Let’s Begin!!! .

4-1 Graphing Polynomial Functions

Jeopardy Q $100 Q $100 Q $100 Q $100 Q $100 Q $200 Q $200 Q $200

3.1 Polynomials How do I know if it’s a polynomial?

4.3: Polynomial Functions

Let’s Review Functions

Polynomial Functions What you’ll learn

Polynomial Functions Chapter 7, Sections 1 and 2.

Polynomial Functions Unit 5 Algebra 2A.

Evaluate and Graph Polynomial Functions

5.2B Graphing Polynomial Functions

Polynomial Functions and Graphs

6.2 Evaluate and Graph Polynomial Functions

Let’s Begin!!! .

5.3 Polynomial Functions.

5.2A Evaluating Polynomial Functions

Evaluate the expression when x = –4

Presentation transcript:

5.2 Evaluate and Graph Polynomial Functions

The degree of the polynomial. A polynomial function is a function of the form: This is called the lead coefficient. The constant term All the exponents are whole numbers.

Here is a summary of common types of polynomial functions. Degree Type Standard Form Constant 1 Linear 2 Quadratic 3 Cubic 4 Quartic

Recall to evaluate a polynomial you could use direct substitution. For example evaluate: when x = 3. Here is another way to evaluate a polynomial function called synthetic substitution: 2 0 -8 5 -7 3 x-value ADD 105 6 18 30 10 35 98 6 Mult. By 3 2 f(3)=98

Use synthetic substitution to evaluate the polynomial at the given value. Check your result by direct substitution.

Here are 4 graphs: Notice for each as: and We call this the “end behavior” of a polynomial function; that is the value (y) of a function as x approached positive infinity and negative infinity.

Here are 4 more graphs: Notice again for each as: and We call this the “end behavior” of a polynomial function; that is the value (y) of a function as x approached positive infinity and negative infinity.

n even n odd For polynomial functions: The end behavior is determined by the lead coefficient and degree. n even n odd