5.2 Polynomials, Linear Factors, and Zeros P288-292.

Slides:



Advertisements
Similar presentations
Warm Up 0?1? 2? Graph the linear functions.0?1? 2?
Advertisements

Notes Over 4.3 Finding Intercepts Find the x-intercept of the graph of the equation. x-intercept y-intercept The x value when y is equal to 0. Place where.
Polynomial Functions Section 2.3. Objectives Find the x-intercepts and y-intercept of a polynomial function. Describe the end behaviors of a polynomial.
Basics of a Polynomial.
Power Functions and Models; Polynomial Functions and Models February 8, 2007.
3.2 Intercepts. Intercepts X-intercept is the x- coordinate of a point when the graph cuts the x-axis Y-intercept is the y- coordinate of a point when.
Section 2.3: Polynomial Functions of Higher Degree with Modeling April 6, 2015.
1. Determine if f(x) has a minimum or maximum 2. Find the y-intercept of f(x) 3. Find the equation of the axis of symmetry of f(x) 4. Find the vertex of.
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.
Chapter 3 Section 3.2 Polynomial Functions and Models.
Warm-up:. Homework: 7.5: graph secant, cosecant, tangent, and cotangent functions from equations (6-7) In this section we will answer… What about the.
By Noureen Villamar Melissa Motieram Elizabeth Stasiak Period B.
Find the x and y intercepts of each graph. Then write the equation of the line. x-intercept: y-intercept: Slope: Equation:
WRITING LINEAR EQUATIONS FINDING THE X-INTERCEPT AND Y- INTERCEPT.
Warm Up: Solve & Sketch the graph:. Graphing Polynomials & Finding a Polynomial Function.
Polynomial Functions Zeros and Graphing Section 2-2.
 Announcements: Mandatory office hours to clear missing homework this Saturday. Do Now.
6.2 Polynomials and Linear Functions
Start Up Day 14 WRITE A POLYNOMIAL FUNCTION OF MINIMUM DEGREE WITH INTEGER COEFFICIENTS GIVEN THE FOLLOWING ZEROS:
Solving Polynomial Equations in Factored Form Lesson 10.4A Algebra 2.
Finding the equation of a Polynomial from the roots and a Graph.
Warm Up I can find x- and y-intercepts given an equation.
 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.
THE SLIDES ARE TIMED! KEEP WORKING! YOUR WORK IS YOUR OWN! Quadratic Systems Activity You completed one in class… complete two more for homework.
Graphing Polynomials. Step One: Determine End Behavior Using Lead Coefficient Test.
Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.
Characteristics of Polynomials: Domain, Range, & Intercepts
7.3 – Writing Equations in Slope Intercept Form Objective(s): to write a linear equation in slope-intercept form given the slope and y-intercept Standard(s):
6-2 Polynomials and Linear Factors. Standard and Factored Form  Standard form means to write it as a simplified (multiplied out) polynomial starting.
Algebra 2/TrigonometryName: __________________________ 6.6 WorksheetDate: ________________ Block: _____ For each polynomial, complete the following: (a)
Bell Ringer. Zeroes of Polynomials October 28, 2015.
17 A – Cubic Polynomials 3: Graphing Cubics from General Form.
5-2 Polynomials, Linear Factors, & Zeros
Analyze the factored form of a polynomial by using the zero-product property. 5-2 POLYNOMIALS, LINEAR FACTORS, AND ZEROS.
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.
Topic 5 Objectives After completing the topic Polynomial functions, students will be able to understand the relationship between the degree of a polynomial.
When an equation is in slope-intercept form: Examples: Identify the slope of the line and the y- intercept for each equation. 1. y = 3x y = ½.
CC1 Key Features of a Graph Domain? Range? End-Behavior? Maximum? Minimum? Interval of Increase? Interval of Decrease?
5.2 Polynomials, Linear Factors, and Zeros
Unit 9 Review Find the equation of the axis of symmetry, along with the coordinates of the vertex of the graph and the y-intercept, for the following equation.
Review 2-1 and 2-2. Quiz Overview (non-calculator) 2-1a) graph power functions (4 points, 8 matching) b) solve radical equations (4 points, 2 equations)
4.2 Polynomial Functions and Models. A polynomial function is a function of the form.
5.2 Polynomial & Linear Factors Learning goals graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using.
Linear Functions and Slope
Section 5.7 Ax+By=C Form Definitions of the Day (DODs) 1. Ax+By=C Form 2. X-Intercept 3. Y-Intercept.
Graphing Linear Equations In Standard Form Ax + By = C.
Unit 3. Day 10 Practice Graph Using Intercepts.  Find the x-intercept and the y-intercept of the graph of the equation. x + 3y = 15 Question 1:
Big Idea: -Graph quadratic functions. -Demonstrate and explain the effect that changing a coefficient has on the graph. 5-2 Properties of Parabolas.
5-1 Graphing Quadratic Functions Algebra II CP. Vocabulary Quadratic function Quadratic term Linear term Constant term Parabola Axis of symmetry Vertex.
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.
Lesson 2.2 Read: Pages Page 112: #1-9 (EOO), (EOO), (EOO)
Interpreting Various Forms of Quadratic Equations (2.1.2) October 2nd, 2015.
PreCalculus 4-R Unit 4 Polynomial and Rational Functions Review Problems.
Integrated Mathematics. Objectives The student will be able to:: 1. graph linear equations. 2. write equations in point- slope form.
Grudgeball! Unit 4 (Part 2) Test Review. Factor completely:
Factors, Roots, Zeros For a Polynomial Function: The Factors are:(x + 5) and (x - 3) The Zeros are -5 and 3 The x-intercepts are at: -5 or 3 The Roots/Solutions.
7-3 Linear Equations and Graphs 9P2: Translate between tables, graphs and functions.
3.1 Polynomial Functions and their Graphs. f(x) = 3x 5 + 6x 4 – 2x 3 + 7x - 6.
5-2 Polynomials, Linear Factors, & Zeros
Warmup 3-7(1) For 1-4 below, describe the end behavior of the function. -12x4 + 9x2 - 17x3 + 20x x4 + 38x5 + 29x2 - 12x3 Left: as x -,
6.5/6.8 Analyze Graphs of Polynomial Functions
4.2 Properties of Polynomial Graphs
Warm Up Graph the following y= x4 (x + 3)2 (x – 4)5 (x – 3)
Warm Up Graph the following y= x4 (x + 3)2 (x – 4)5 (x – 3)
Lesson 5.8 Graphing Polynomials.
4.3: Polynomial Functions
Review Write the product of the sum and difference. (x + 3) (x – 3)
 .
Section – Linear Programming
Polynomial Functions of Higher Degree
Presentation transcript:

5.2 Polynomials, Linear Factors, and Zeros P

Review) Determine end behavior.

Ex) Write the polynomial in factored form. Then find the zeros (these are values of x that make the equation =0…also called x-intercepts). State the multiplicity of multiple zeros.

Ex) Sketch the graph by determining end- behavior, finding zeros and the y-intercept

Ex) Write a polynomial function in standard form with the given zeros: a) -2, 2, and 3.

Ex) Write a polynomial function in standard form with the given zeros: b) -2, -2, 2 and 3.

Ex) Find the zeros. State the multiplicity of multiple zeros.

Ex) Find the relative maximum and relative minimum of the graph.

Ex) Find the relative maximum and relative minimum of the graph.