BY MAHRA Graphs of Polynomials. What types of polynomial graphs are there? First-degree polynomial. Second-degree, or quadratic, polynomial. Higher degree.

Slides:

Advertisements

Similar presentations

Warm Up 1.Write the standard form of the quadratic function given a vertex and a point: vertex : (-4,-1) point: (-2,4) 2. State the vertex of the following.

Advertisements

If the leading coefficient of a quadratic equation is positive, then the graph opens upward. axis of symmetry f(x) = ax2 + bx + c Positive #

Essential Question(s): How can you tell if a quadratic function a) opens up or down b) has a minimum or maximum, and c) how many x-intercepts it has?

MAT 150 – CLASS #20 Topics: Identify Graphs of Higher-Degree Polynomials Functions Graph Cubic and Quartic Functions Find Local Extrema and Absolute Extrema.

Polynomial Functions Section 2.3. Objectives Find the x-intercepts and y-intercept of a polynomial function. Describe the end behaviors of a polynomial.

Section 7.5 – Graphing Quadratic Functions Using Properties.

Warm-Up: December 15, 2011  Divide and express the result in standard form.

Power Functions and Models; Polynomial Functions and Models February 8, 2007.

Quadratic Functions and Models

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 4.3 Quadratic Functions and Their Properties.

Essential Question: How do you determine whether a quadratic function has a maximum or minimum and how do you find it?

And the Quadratic Equation……

4.3 G RAPHS OF P OLYNOMIAL F UNCTIONS Objectives: 1. Recognize the shape of basic polynomial functions. 2. Describe the graph of a polynomial function.

Analyzing Graphs of Polynomials Section 3.2. First a little review… Given the polynomial function of the form: If k is a zero, Zero: __________ Solution:

Copyright © Cengage Learning. All rights reserved. Quadratic Equations, Quadratic Functions, and Complex Numbers 9.

Slides for 2/9 & 2/10 Precalculus. Warm-Up Set 9 Problem 2 Using your calculator, find a line of regression for the following data set, and find the correlation.

Section 2.3: Polynomial Functions of Higher Degree with Modeling April 6, 2015.

Properties of Quadratics Chapter 3. Martin-Gay, Developmental Mathematics 2 Introduction of Quadratic Relationships  The graph of a quadratic is called.

MAT 150 – Class #20 Topics: Identify Graphs of Higher-Degree Polynomials Functions Graph Cubic and Quartic Functions Find Local Extrema and Absolute Extrema.

The axis of symmetry is x = h. This is the vertical line that passes through the vertex. 3.1 – Quadratic Functions and Application Quadratic Functions.

Quadratic Functions Objectives: Graph a Quadratic Function using Transformations Identify the Vertex and Axis of Symmetry of a Quadratic Function Graph.

Getting Ready: Zero Product Property If two numbers multiply together to equal zero, one or both of the numbers must equal zero. ie) m x n = 0  m or n.

Holt McDougal Algebra Properties of Quadratic Functions in Standard Form This shows that parabolas are symmetric curves. The axis of symmetry is.

9.4 Graphing Quadratics Three Forms

Chapter 3 – Polynomial and Rational Functions Polynomial Functions and Their Graphs.

Chapter 2.  A polynomial function has the form  where are real numbers and n is a nonnegative integer. In other words, a polynomial is the sum of one.

9.1: GRAPHING QUADRATICS ALGEBRA 1. OBJECTIVES I will be able to graph quadratics: Given in Standard Form Given in Vertex Form Given in Intercept Form.

Precalculus Lesson 2.2 Polynomial Functions of Higher Degree.

 Graph is a parabola.  Either has a minimum or maximum point.  That point is called a vertex.  Use transformations of previous section on x 2 and -x.

2.3 Quadratic Functions. A quadratic function is a function of the form:

Math 160 Notes Packet #7 Polynomial Functions 1. 2.

2.1 – Quadratic Functions.

Essential Question: How do you sketch the graphs of polynomial functions? Students will write a summary of how to sketch a graph of a polynomial function.

The Graphs of Polynomials

Graphing Polynomials. Total number of roots = __________________________________. Maximum number of real roots = ________________________________. Maximum.

Analyzing Graphs of Polynomials

5.2 Polynomials, Linear Factors, and Zeros P

Analyze the factored form of a polynomial by using the zero-product property. 5-2 POLYNOMIALS, LINEAR FACTORS, AND ZEROS.

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

Warm Up Are the following graphs even or odd? (Draw them on your paper) 2.What are the zeros for the given polynomial function and what is the multiplicity.

Section 3.1 Review General Form: f(x) = ax 2 + bx + c How the numbers work: Using the General.

Graphing Parabolas Students will be able to graph parabolas or second degree equations.

Working With Quadratics M 110 Modeling with Elementary Functions Section 2.1 Quadratic Functions V. J. Motto.

4.2 Polynomial Functions and Models. A polynomial function is a function of the form.

1 Solving Quadratic Equations 1Shaw 2008 February 16, 2010.

Do Now: Solve the equation in the complex number system.

Quadratic Functions. 1. The graph of a quadratic function is given. Choose which function would give you this graph:

F(x) = x 2 Let’s review the basic graph of f(x) = x xf(x) = x

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 5.1 Polynomial Functions and Models.

For each polynomials, follow all the steps indicated below to graph them: (a) Find the x- and y-intercepts of f. (b) Determine whether the graph of f crosses.

 Polynomial Functions of Higher Degree.  Use transformations to sketch graphs of polynomial functions.  Use the Leading Coefficient Test to determine.

Interpreting Various Forms of Quadratic Equations (2.1.2) October 2nd, 2015.

Do Now: Solve the equation in the complex number system.

Graphing Quadratic Functions. The graph of any Quadratic Function is a Parabola To graph a quadratic Function always find the following: y-intercept.

Quadratic Functions Lesson 3.3. Quadratic Function  Degree 2  Parabola shaped  Can open upward or downward  Always has a vertex which is either the.

PreCalculus 4-R Unit 4 Polynomial and Rational Functions Review Problems.

Key Components for Graphing a Quadratic Function.

Copyright © Cengage Learning. All rights reserved.

Parabolas Because you need them, for physics and stuff.

Warm-Up 1. Find the -Vertex -Y-Intercept -X-intercepts 2. Graph 3. Factor.

Unit 3-1: Higher-Degree Polynomials Functions Topics: Identify Graphs of Higher-Degree Polynomials Functions Graph Cubic and Quartic Functions Find Local.

Notes 4.3 Graphs of Polynomial Functions

Quadratic Functions In Chapter 3, we will discuss polynomial functions

Notes 3.3 Quadratic Functions

4.3 Graphs of Polynomial Functions

Quadratic Functions.

Objectives Find the zeros of a quadratic function from its graph.

Drawing Quadratic Graphs

Polynomial Functions of Higher Degree

Presentation transcript:

BY MAHRA Graphs of Polynomials

What types of polynomial graphs are there? First-degree polynomial. Second-degree, or quadratic, polynomial. Higher degree polynomials.

How to draw a first-degree polynomial?

How to draw a second-degree polynomial? It is basically a parabola. It can open either upward (positive) or downward (negative). It always has a vertex (minimum or maximum). Always has 1 y-intercepts and 0,1 or 2 x-intercepts. For example:

How to draw a higher-degree polynomial?

In Odd Polynomials

In Even Polynomials

What are some special properties for polynomial functions? 1. Every graph of a polynomial is continuous, meaning that there should be no holes, gaps or jumps. 2. The graph also should not have a sharp corner. Example: Correct Not a polynomial

Zero-31 Multiplicity213

Zero23 Multiplicity213 TouchesCrosses

6. Local extrema, which means either a local minimum or a local maximum. 7. Points of inflection.

Bibliography aylorPolynomials/OverlayOfRose3.gif Linear_functions2.PNG Functions/04_Polynomial-Functions/ My Pre-Calculus Book. Some pictures are from Google.

Thank you for listening. THEENDTHEEND