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

Slides:



Advertisements
Similar presentations
Factoring the Sum or the Difference of Two Cubes. Subtitle: Know the CARD!!!
Advertisements

5.5: Polynomial Long Division and Synthetic Division
Solving Equations = 4x – 5(6x – 10) -132 = 4x – 30x = -26x = -26x 7 = x.
Finding the Intercepts of a Line
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.
X and Y Intercepts. Definitions Intercept – the point where something intersects or touches.
What is the slope? undefined. What is the slope? m = -1.
Solve Equations by Factoring Section 6.4 MATH Mr. Keltner.
Basic Functions and Their Graphs
Power Functions and Models; Polynomial Functions and Models February 8, 2007.
Find the x-intercept To find the y-intercept, we must use 0 for x. Substitute x = 0 into 2x + 3y = 6 and solve for y: 2x + 3y = 6 2(0) + 3y = y.
POLYNOMIAL FUNCTIONS AND MODELS
Roots & Zeros of Polynomials I How the roots, solutions, zeros, x-intercepts and factors of a polynomial function are related.
4.4 Rational Functions Objectives:
Quadratic Functions Objectives: Graph a Quadratic Function using Transformations Identify the Vertex and Axis of Symmetry of a Quadratic Function Graph.
Graphing polynomials To graph a polynomial we need to know three things 1) Type of polynomial 2) Roots 3) y-intercept.
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.
Today in Pre-Calculus Go over homework Notes: Homework
Chapter 2 Examples Section 2 Linear Functions. Objective: Students will identify patterns with linear forms of equations and functions. They will also.
Section 6-2: Polynomials and Linear Factors
Academy Algebra II/Trig 5.5: The Real Zeros of a Polynomial Functions HW: p.387 (14, 27, 30, 31, 37, 38, 46, 51)
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.
Solving Polynomial Equations Section 4.5 beginning on page 190.
Finding the equation of a Polynomial from the roots and a Graph.
The x-intercept of a line is the point (a,0) where the line intersects the x-axis. x and y Intercepts (a,0)
Section 2.4 – Circles Circle – a set of points in a plane that are equidistant from a fixed point.
Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.
An equation in the form … … can be solved using two methods discussed previously. Solving Equations Containing Trinomials 1.Factoring Method 2.Graphing.
Section 5.5 The Real Zeros of a Polynomial Function.
6-2 Polynomials and Linear Factors. Standard and Factored Form  Standard form means to write it as a simplified (multiplied out) polynomial starting.
Section 5.3 Solving Systems of Equations Using the Elimination Method There are two methods to solve systems of equations: The Substitution Method The.
Sullivan Algebra and Trigonometry: Section 5.1 Polynomial Functions Objectives Identify Polynomials and Their Degree Graph Polynomial Functions Using Transformations.
17 A – Cubic Polynomials 3: Graphing Cubics from General Form.
Solving equations with polynomials – part 2. n² -7n -30 = 0 ( )( )n n 1 · 30 2 · 15 3 · 10 5 · n + 3 = 0 n – 10 = n = -3n = 10 =
5.2 Polynomials, Linear Factors, and Zeros P
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.
Solving Equations Binomials Simplifying Polynomials
By the end of this section, you will be able to: 1. Determine the number and type of roots for a polynomial equation; 2. Find the zeros of a polynomial.
Chapter 6 – Polynomials and Polynomial Functions 6.6 –Polynomials of Greater Degree.
CC1 Key Features of a Graph Domain? Range? End-Behavior? Maximum? Minimum? Interval of Increase? Interval of Decrease?
Warmup Divide using synthetic division using the zero given. Then factor the answer equation completely and solve for the remaining zeroes. Show.
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.
Solving Polynomials.
Section 5.7 Ax+By=C Form Definitions of the Day (DODs) 1. Ax+By=C Form 2. X-Intercept 3. Y-Intercept.
Section 4.2 Graphing Polynomial Functions Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.
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:
Standard Form Objective: To graph the equation of a line in Standard Form from give information. Warm – up: Write the following equations in Standard Form.
SECTION 6-6: POLYNOMIALS OF GREATER DEGREE Goal: Factor polynomials and solve polynomial equations of degree greater than three.
Conjugate Pairs Theorem Every complex polynomial function of degree n  1 has exactly n complex zeros, some of which may repeat. 1) A polynomial function.
Section 4.1 Polynomial Functions and Models.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 5.1 Polynomial Functions and Models.
Section 3-7 Investigating Graphs of Polynomial Functions Objectives: Use properties of end behavior to analyze, describe, and graph polynomial functions.
Notes Over 10.4 Zero-Product Property if the product of two factors is zero, then at least one of the factors must be zero.
3.1 Polynomial Functions and their Graphs. f(x) = 3x 5 + 6x 4 – 2x 3 + 7x - 6.
Determine the x and y intercepts. Find the card that matches.
Solving Higher Degree Polynomial Equations.
Notes Over 3.4 The Rational Zero Test
Warm Up - September 27, 2017 Classify each polynomial by degree and by number of terms. 1. 5x x2 + 4x - 2 Write each polynomial in standard form.
Polynomial Functions and Their Graphs
Solving Percent Problem with Equations
2.6 Section 2.6.
Section 6.3 – Polynomial Division
Polynomial Functions and Models
Section 2.3: Polynomial Functions of Higher Degree with Modeling
Objective SWBAT solve polynomial equations in factored form.
The Real Zeros of a Polynomial Function
Presentation transcript:

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

General Shape of Polynomial Functions

Standard vs. Factored Form General Shape Y-intercept General Shape X-intercept(s)

Multiplicities of Zeros Multiplicity of 1 Multiplicity of 2 Multiplicity of 3

Identifying Degrees and Zeros

Solve.

Given the zeros, write an equation for each polynomial in standard form. Zeros: -6, 1, 9 Zeros:

Mix-and-Match Activity If you were given a card with zeros, write the equation for the polynomial in standard form. If you were given a card with an equation of a polynomial, determine the zeros of the function. NOW, find the person that you match up with.