6.1 Polynomial Functions, Part II

Nov 23, 2013

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6.1 Polynomial Functions, Part II

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Polynomial Functions

Polynomial Functions. Lesson 9.2. Polynomials. Definition: The sum of one or more power function Each power is a non negative integer. Polynomials. General formula a 0 , a 1 , … ,a n are constant coefficients n is the degree of the polynomial

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Polynomial Functions

Polynomial Functions. To the n th degree!. What are we trying to do?. Be able to look at any single-variable (only x, or only y, or only µ, or whatever) polynomial equation and be able to tell: The degree (should be review) The number of maxima or minima (Points of Inflection)

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Polynomial Functions

Polynomial Functions. Karen Huie. Trey Gibson. Brittani Cartner. Polynomial Functions. What are Polynomial functions? Definition: Polynomial functions are defined and continuous on all real numbers.

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Polynomial Functions

Degree Name Example 0 Constant Linear Quadratic Cubic Quartic Quintic. 5. Polynomial Functions. -. +. 2. x. 4x. 3=0. 2 nd Degree Polynomials and the Zeros of the Function. Factor the polynomial and find the points At which the function equals zero.

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Polynomial Functions

Polynomial Functions. Polynomial Functions. A polynomial is a monomial or the sum of monomials. A Polynomial Function: P(x) = a n x n + a n-1 x n-1 + … + a 1 x + a 0 Where n is a nonnegative integer and the coefficients a n …a 0 are real numbers. Standard Form of a Polynomial.

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Polynomial Functions

Polynomial Functions. What are they?. Polynomial Functions. Transformations: are the same as transformations for any function y = a f(k(x-d)) + c Reflections occur is either a or k are negative a= vertical stretch by a factor of absolute a k= horizontal stretch by a factor of absolute k

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Polynomial Functions

Polynomial Functions. February 27,2012. What is a polynomial function?. What is a polynomial? The sum or difference of two or more algebraic terms (monomials) A polynomial equation used to represent a function is called a polynomial function Example: f(x) = 4x 2 – 3x + 2

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Polynomial Functions

Polynomial Functions. 1. Definitions. 2. Degrees. 3. Graphing. Definitions. Polynomial Monomial Sum of monomials Terms Monomials that make up the polynomial Like Terms are terms that can be combined. Degree of Polynomials. Simplify the polynomial Write the terms in descending order

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Polynomial Functions

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 1 +a 0. A power function. A power function of degree n is a function in the form f(x) = ax n where a is a real number, a ≠ 0 and n > 0 is an integer.

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Polynomial Functions

Polynomial Functions. Polynomial Functions. An equation having a variable raised to an exponent of a non negative integer Degree: the highest power on the variable i.e. f(x) = x 2 + 1 f(x) = x 3 + 1 f(x) = x + 2 f(x) = 3. second degree. third degree. first degree.

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Polynomial Functions

Polynomial Functions. PPT 2.3.1. Polynomial Functions. The largest exponent within the polynomial determines the degree of the polynomial. Explore Polynomials. Linear Function. Quadratic Function. Cubic Function. Quartic Function. Leading Coefficient.

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Polynomial functions

Polynomial functions. Chapter 5. 5.1 – exploring the graphs of polynomial functions. Chapter 5. Polynomial functions. What’s a polynomial?.

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POLYNOMIAL FUNCTIONS

POLYNOMIAL FUNCTIONS. A POLYNOMIAL is a monomial or a sum of monomials. A POLYNOMIAL IN ONE VARIABLE is a polynomial that contains only one variable. Example: 5x 2 + 3x - 7. POLYNOMIAL FUNCTIONS. The DEGREE of a polynomial in one variable is the greatest exponent of its variable.

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Polynomial Functions

Polynomial Functions. AFM Objective 1.01. Polynomial Functions. Polynomials have more than one term: 2x + 1 3x 2 + 2x + 1 The fancy explanation: f(x) = a n x n + a n-1 x n-1 + …+ a 2 x 2 + a 1 x + a Ex: 4x 3 + 3x 2 + 2x + 1

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Polynomial Functions

Polynomial Functions. E VALUATING P OLYNOMIAL F UNCTIONS. a n. n. n. n – 1. a 0. a n  0. leading coefficient. a n. constant term. degree. a 0. n. descending order of exponents from left to right. A polynomial function is a function of the form.

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Polynomial Functions

Simplify each expression by combining like terms. 1. 3 x + 5 x – 7 x 2. –8 xy 2 – 2 x 2 y + 5 x 2 y 3. –4 x + 7 x 2 + x Find the number of terms in each expression. 4. bh 5. 1 – x 6. 4 x 3 – x 2 – 9. 1 2. Polynomial Functions. ALGEBRA 2 LESSON 6-1.

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6.1 Polynomial Functions

6.1 Polynomial Functions. Monomial – an expression that is either a variable, a real number or the product of a real number and variables with whole number exponents. Polynomial – a monomial or the sum of monomials Degree – the sum of the exponents of a term

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Polynomial Functions

Polynomial Functions. Remember integers are … –2, -1, 0, 1, 2 … (no decimals or fractions) so positive integers would be 0, 1, 2 …. A polynomial function is a function of the form:. n must be a positive integer. All of these coefficients are real numbers.

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Polynomial Functions

Polynomial Functions. Information. Graphs of the form y = kx n. Cubic functions. parent function:. f ( x ) = x 3. none. vertical asymptote:. none. horizontal asymptote:. domain:. (– ∞ , ∞ ). (– ∞ , ∞ ). range:. roots:. x = 0. Using a table of values.

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Polynomial Functions

Polynomial Functions. Essential Question:. How do we decide for the degree of the polynomial with a variable? How do we determine the end behavior of a polynomial function?. CCSS: F.IF.4.

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POLYNOMIAL FUNCTIONS

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Polynomial Functions

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