Higher Degree Polynomial.  Case 1: If n is odd AND the leading coefficient, is positive, the graph falls to the left and rises to the right  Case 2:

Slides:

Advertisements

Similar presentations

Polynomial Functions and Their Graphs

Advertisements

Polynomial Functions and Their Graphs

Polynomial Functions A polynomial in x is a sum of monomials* in x.

Table of Contents Polynomials: Multiplicity of a Zero The polynomial, P(x) = x 3 – x 2 – 21x + 45, factors as, P(x) = (x – 3)(x – 3)(x + 5). Its zeros.

The “zero” of a function is just the value at which a function touches the x-axis.

Warm Up Add or Subtract the following polynomials: 1.(2x 2 – 4y + 7xy – 6y 2 ) – (-3x 2 + 5y – 4xy + y 2 ) 2.If P = 4x 4 - 3x 3 + x 2 - 5x + 11 and Q.

Section 5.5 – The Real Zeros of a Rational Function

The “zero” of a function is just the value at which a function touches the x-axis.

Chapter Polynomials of Higher Degree. SAT Problem of the day.

6.2 Graphs of Polynomials. The Degree of Polynomials The degree of a polynomial is the value of the largest exponent. y = 5x 4 + 3x 2 – 7 Degree = 4 y.

$1 Million $500,000 $250,000 $125,000 $64,000 $32,000 $16,000 $8,000 $4,000 $2,000 $1,000 $500 $300 $200 $100 Welcome.

Warm Up Solve using synthetic OR long division Polynomial Functions A polynomial is written in standard form when the values of the exponents are.

Polynomial Functions A function defined by an equation in the form where is a non-negative integer and the are constants.

Notes Over 3.2 Graphs of Polynomial Functions Continuous Functions Non-Continuous Functions Polynomial functions are continuous.

6.3 – Evaluating Polynomials. degree (of a monomial) 5x 2 y 3 degree =

2.3 Polynomial Functions & Their Graphs Objectives –Identify polynomial functions. –Recognize characteristics of graphs of polynomials. –Determine end.

7.1 and 7.2 Graphing Inequalities 7.3 Solving Equations Using Quadratic Techniques Algebra II w/ trig.

Warm Up: Solve & Sketch the graph:. Graphing Polynomials & Finding a Polynomial Function.

Polynomial Functions Zeros and Graphing Section 2-2.

Warm-Up 5/3/13 Homework: Review (due Mon) HW 3.3A #1-15 odds (due Tues) Find the zeros and tell if the graph touches or crosses the x-axis. Tell.

Unit 3 Review for Common Assessment

Factor Theorem & Rational Root Theorem

Solving Polynomial Equations Section 4.5 beginning on page 190.

Welcome to MM250 Unit 6 Seminar: Polynomial Functions To resize your pods: Place your mouse here. Left mouse click and hold. Drag to the right to enlarge.

Quadratic Functions (3.1). Identifying the vertex (e2, p243) Complete the square.

A3 3.2b zeros of polynomials, multiplicity, turning points

Today in Pre-Calculus Go over homework Notes: (need calculator & book)

Evaluate and graph polynomial functions. GOALS: “” Algebra 2: Notes 5.2: End Behavior of Polynomials: Zeros of Polynomials: If P is a polynomial and if.

Polynomial Functions and Their Graphs

3.2 Graphs of Polynomial Functions of Higher Degree.

Section 2.2 Polynomial Functions Of Higher Degree.

 Yes, the STEELERS LOST yesterday!. Graphs of Polynomial Functions E.Q: What can we learn about a polynomial from its graph?

WARM-UP: 10/30/13 Find the standard form of the quadratic function. Identify the vertex and graph.

7.4 Solving Polynomial Equations

Sec 3.1 Polynomials and Their Graphs (std MA 6.0) Objectives: To determine left and right end behavior of a polynomial. To find the zeros of a polynomial.

STEPS: x4 + 3x3 – 12x2 + 12x < 0 x(x – 2)2 (x + 3) < 0

Sect. 2-3 Graphing Polynomial Functions Objectives: Identify Polynomial functions. Determine end behavior recognize characteristics of polynomial functions.

Objectives: 1. Use the factor theorem. 2. Factor a polynomial completely.

ZEROS=ROOTS=SOLUTIONS Equals x intercepts Long Division 1. What do I multiply first term of divisor by to get first term of dividend? 2. Multiply entire.

7.1 Polynomial Functions Evaluate Polynomials

SFM Productions Presents: Another day of Pre-Calculus torture! No fun for you - tons of fon for me! 2.2 Polynomial Functions of Higher Degree.

Polynomials of Higher Degree 2-2. Polynomials and Their Graphs  Polynomials will always be continuous  Polynomials will always have smooth turns.

Graphing Polynomial Functions. Finding the End Behavior of a function Degree Leading Coefficient Graph Comparison End Behavior As x  – , Rise right.

AFM Objective  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.

Chapter 5. Polynomial Operations.

Section 2.2 Polynomial Functions of Higher Degree.

Functions. Objectives: Find x and y intercepts Identify increasing, decreasing, constant intervals Determine end behaviors.

Polynomials Graphing and Solving. Standards MM3A1. Students will analyze graphs of polynomial functions of higher degree. a. Graph simple polynomial functions.

Polynomial Functions and Their Graphs. Definition of a Polynomial Function Let n be a nonnegative integer and let a n, a n- 1,…, a 2, a 1, a 0, be real.

Chapter 2 – Polynomial and Rational Functions 2.2 – Polynomial Functions of Higher Degree.

Example 4. The daily cost of manufacturing a particular product is given by where x is the number of units produced each day. Determine how many units.

Section 3.3 Dividing Polynomials; Remainder and Factor Theorems

Factor Theorem & Rational Root Theorem

Factor Theorem & Rational Root Theorem

5.6 Find The Rational Zeros

Aim #3. 3 How do we divide Polynomials

Section 3.3 Dividing Polynomials; Remainder and Factor Theorems

2.2 Polynomial Functions of Higher Degree

Warm Up Graph the following y= x4 (x + 3)2 (x – 4)5 (x – 3)

Warm-up Complete this as a group on you Board. You have 15 minutes

Factor Theorem & Rational Root Theorem

Warm Up Graph the following y= x4 (x + 3)2 (x – 4)5 (x – 3)

Graph Polynomials Effect of Multiplicity on a graph

Functions AII.7 cdf 2009.

Factor Theorem & Rational Root Theorem

Warm-up: Determine the left and right-hand behavior of the graph of the polynomial function, then find the x-intercepts (zeros). y = x3 + 2x2 – 8x HW:

Graph Polynomials Effect of Multiplicity on a graph

Polynomial Functions of Higher Degree

Section 3.3 Dividing Polynomials; Remainder and Factor Theorems

Presentation transcript:

Higher Degree Polynomial

 Case 1: If n is odd AND the leading coefficient, is positive, the graph falls to the left and rises to the right  Case 2: If n is odd AND the leading coefficient, is negative, the graph rises to the left and falls to the right.  Case 3: If n is even AND the leading coefficient, is positive, the graph rises to the left and to the right.  Case 4: If n is even AND the leading coefficient, is negative, the graph falls to the left and to the right.

Even functions will have the same end behaviors. Odd functions will have opposite end behaviors.

 The degree of your polynomial will be the highest degree in the polynomial. When in standard form it will be the degree of the first term. Ex: f(x)=x 5 +2x 2 +4x The degree of this polynomial is 5. There will be five zeros.

The zeros of a polynomial function are the points where the graph crosses the x-axis. They can also be found by setting the function to zero and solving for your x term. You may also need to use synthetic division to solve the function.

Repeated zeros are also known as bouncers. They are marked on a graph when the graph hits the x-axis and immediately “bounces” back up without actually crossing the x-axis. When you solve the equation above you get 0=(x-1)(x-1), solve that and you get x=1, 1. Since there are repeating zeros, or solutions, the graph “bounces”.

 mages/solution-1-by-0-graph.gif mages/solution-1-by-0-graph.gif  gif gif  cs/end_beh.jpg cs/end_beh.jpg  math/mathlab/col_algebra/col_alg_tut35_pol yfun.htm math/mathlab/col_algebra/col_alg_tut35_pol yfun.htm