Presentation is loading. Please wait.

Presentation is loading. Please wait.

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

Published byTodd Freeman Modified over 8 years ago

Similar presentations

Presentation on theme: "2.1 Evaluate and Graph Polynomial Functions Objectives: Identify, evaluate, add, and subtract polynomials Classify polynomials, and describe the shapes."— Presentation transcript:

1 2.1 Evaluate and Graph Polynomial Functions Objectives: Identify, evaluate, add, and subtract polynomials Classify polynomials, and describe the shapes of their graphs

2 What is a Polynomial? 1 or more terms Exponents are whole numbers (not a radical) Coefficients are all real numbers (no imaginary #’s) It is in Standard Form when the exponents are written in descending order.

3 Definitions for Polynomials Monomial: a numeral, variable, or the product of a numeral and one or more variables Ex: Constant: a monomial w/ no variables Ex: Coefficient: numerical factor in a monomial Ex: Degree of a Monomial: sum of exponents of its variables Ex: See Below Give the degree for the following monomial. 4x 2 y 3 z _________ ab 4 c 2 ________ 8 ________ NOT QUOTIENT! i.e. “x” can’t be on bottom!!!! 6 7 0

4 Polynomial: is many (more than 1) monomials connected by addition or subtraction. Definitions for Polynomials Binomial - ___________ Trinomial - ______________ Degree of the Polynomial: is the degree of it’s highest monomial term Example: Give the degree of the polynomial. 4x 3 + 6x 2 -8x 5 – 6 ________ (5x + 4)(2x 2 + 3x – 2)

5 Classification of a Polynomial DegreeNameExample -2x 5 + 3x 4 – x 3 + 3x 2 – 2x + 6 n = 0 n = 1 n = 2 n = 3 n = 4 n = 5 constant 3 linear 5x + 4 quadratic 2x 2 + 3x - 2 cubic 5x 3 + 3x 2 – x + 9 quartic 3x 4 – 2x 3 + 8x 2 – 6x + 5 quintic

6 Classify each polynomial by degree and by number of terms. a) 5x + 2x 3 – 2x 2 cubic trinomial b) x 5 – 4x 3 – x 5 + 3x 2 + 4x 3 quadratic monomial c) x 2 + 4 – 8x – 2x 3 d) 3x 3 + 2x – x 3 – 6x 5 cubic polynomial quintic trinomial e) 2x + 5x 7 7 th degree binomial Not a polynomial

7 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, type, and leading coefficient. a. h (x) = x 4 – x 2 + 3 1 SOLUTION a. The function is a polynomial function that is already written in standard form. It has degree 4 (quartic) and a leading coefficient of 1.

8 EXAMPLE 1 Identify polynomial functions Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient. b. g (x) = 7x – 3 + πx 2 SOLUTION b. The function is a polynomial function written as g(x) = πx 2 + 7x – 3 in standard form. It has degree 2 (quadratic) and a leading coefficient of π.

9 EXAMPLE 1 Identify polynomial functions Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient. c. f (x) = 5x 2 + 3x –1 – x SOLUTION c. The function is not a polynomial function because the term 3x – 1 has an exponent that is not a whole number.

10 EXAMPLE 1 Identify polynomial functions Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient. d. k (x) = x + 2 x – 0.6x 5 SOLUTION d. The function is not a polynomial function because the term 2 x does not have a variable base and an exponent that is a whole number.

11 GUIDED PRACTICE for Examples 1 and 2 Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient. 1. f (x) = 13 – 2x polynomial function; f (x) = –2x + 13; degree 1, type: linear, leading coefficient: –2 2. p (x) = 9x 4 – 5x – 2 + 4 3. h (x) = 6x 2 + π – 3x polynomial function; h(x) = 6x 2 – 3x + π ; degree 2, type: quadratic, leading coefficient: 6 not a polynomial function

12 EXAMPLE 2 Evaluate by direct substitution Use direct substitution to evaluate f (x) = 2x 4 – 5x 3 – 4x + 8 when x = 3. f (x) = 2x 4 – 5x 3 – 4x + 8 f (3) = 2(3) 4 – 5(3) 3 – 4(3) + 8 = 162 – 135 – 12 + 8 = 23 Write original function. Substitute 3 for x. Evaluate powers and multiply. Simplify

13 GUIDED PRACTICE for Examples 1 and 2 Use direct substitution to evaluate the polynomial function for the given value of x. 4. f (x) = x 4 + 2x 3 + 3x 2 – 7; x = –2 5 ANSWER 5. g(x) = x 3 – 5x 2 + 6x + 1; x = 4 9 ANSWER

14 Solving by Synthetic Substitution (Division) (x - 2) is a Factor of use x = 2 Use the Polynomials coefficients Multiply Answer Add Down Drop 1 st coefficient down Remainder if there is any The Solution starts with one degree less than original

15 HomeworkHomework Pg.69 1 – 20

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

Similar presentations

Turn In GHSGT Worksheet!!.

Turn In GHSGT Worksheet!!.
7.1 An Introduction to Polynomials

7.1 An Introduction to Polynomials
A POLYNOMIAL is a monomial or a sum of monomials.

A POLYNOMIAL is a monomial or a sum of monomials.
Do Now Simplify the expression. Answers to Homework 1) :cubic polynomial of 4 terms 2) :6 th degree trinomial 3) :quartic monomial 4) :quintic binomial.

Do Now Simplify the expression. Answers to Homework 1) :cubic polynomial of 4 terms 2) :6 th degree trinomial 3) :quartic monomial 4) :quintic binomial.
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,

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,
Polynomials and Polynomial Functions Section 5.3.

Polynomials and Polynomial Functions Section 5.3.
Friday February 7, 2014 5.1 Properties of Exponent Objective: To evaluate or simplify expression with powers EQ: Can you multiply and divide negative fraction.

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

EXAMPLE 1 Identify polynomial functions
6.1 Using Properties of Exponents What you should learn: Goal1 Goal2 Use properties of exponents to evaluate and simplify expressions involving powers.

6.1 Using Properties of Exponents What you should learn: Goal1 Goal2 Use properties of exponents to evaluate and simplify expressions involving powers.
7.1 An Introduction to Polynomials Objectives: Identify, evaluate, add, and subtract polynomials. Classify polynomials, and describe the shapes of their.

7.1 An Introduction to Polynomials Objectives: Identify, evaluate, add, and subtract polynomials. Classify polynomials, and describe the shapes of their.
Do Now: Evaluate each expression for x = -2. Aim: How do we work with polynomials? 1) -x + 12) x 2 - 53) -(x – 6) Simplify each expression. 4) (x + 5)

Do Now: Evaluate each expression for x = -2. Aim: How do we work with polynomials? 1) -x + 12) x ) -(x – 6) Simplify each expression. 4) (x + 5)
Introduction to Polynomials

Introduction to Polynomials
An Introduction to Polynomials

An Introduction to Polynomials
Adding & Subtracting Polynomials

Adding & Subtracting Polynomials
Degree The largest exponent Standard Form Descending order according to exponents.

Degree The largest exponent Standard Form Descending order according to exponents.
CHAPTER 3 3-1 polynomials. SAT Problem of the day What is the distance between the origin and the point (-5,9)? A)5.9 B)6.7 C)8.1 D)10.3 E)11.4.

CHAPTER polynomials. SAT Problem of the day What is the distance between the origin and the point (-5,9)? A)5.9 B)6.7 C)8.1 D)10.3 E)11.4.
The first column shows a sequence of numbers. Second column shows the first difference. (-6) – (-4) = -2 If the pattern continues, what is the 8 th number.

The first column shows a sequence of numbers. Second column shows the first difference. (-6) – (-4) = -2 If the pattern continues, what is the 8 th number.
EQ – what is a polynomial, and how can I tell if a term is one?

EQ – what is a polynomial, and how can I tell if a term is one?
CLASSIFYING POLYNOMIALS. A _______________ is a sum or difference of terms. Polynomials have special names based on their _______ and the number of _______.

CLASSIFYING POLYNOMIALS. A _______________ is a sum or difference of terms. Polynomials have special names based on their _______ and the number of _______.
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.

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.

Similar presentations

Ads by Google