200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 SimplifyingRandomWord ProblemsSolvingProperties.

Slides:

Advertisements

Similar presentations

Polynomial Functions and Graphs

Advertisements

EXAMPLE 1 Use x-intercepts to graph a polynomial function Graph the function f (x) = (x + 3)(x – 2) SOLUTION Plot: the intercepts. Because – 3 and.

Finding Real Roots of Polynomial Equations 6-5

Example 4 Solving a Quartic Equation Chapter 6.4 Solve the equation.  2009 PBLPathways.

Do Now Simplify the expression. Answers to Homework 1) :cubic polynomial of 4 terms 2) :6 th degree trinomial 3) :quartic monomial 4) :quintic binomial.

“ARE YOU READY FOR THIS?”. 1. Classify this polynomial by degree: f(x) = 4x³ + 2x² - 3x + 7 a. binomial b. 4 term c. cubic d. quartic How do you know?

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

2.8 Analyzing Graphs of Polynomial Functions p. 373

2.8 Analyze Graphs of Polynomial Functions

10.4 Factoring to solve Quadratics – Factoring to solve Quad. Goals / “I can…”  Solve quadratic equations by factoring.

Section 3-5 Finding Real Roots of Polynomial Equations

By Noureen Villamar Melissa Motieram Elizabeth Stasiak Period B.

Write the equation for transformation of.

Graphs of Polynomial Functions

Write the equation for transformation of.

WRITING LINEAR EQUATIONS FINDING THE X-INTERCEPT AND Y- INTERCEPT.

Ms. C. Taylor Common Core Math 3. Warm-Up Polynomials.

Objectives Identify the multiplicity of roots.

Objectives Identify the multiplicity of roots Use the Rational Root Theorem and the Irrational Root Theorem to solve polynomial equations.

An Introduction to Polynomials

6.8 Analyzing Graphs of Polynomial Functions

Objectives I will use the distributive property to factor a polynomial.

The first column shows a sequence of numbers. Second column shows the first difference. (-6) – (-4) = -2 If the pattern continues, what is the 8 th number.

Classification of a Polynomial DegreeNameExample -2x 5 + 3x 4 – x 3 + 3x 2 – 2x + 6 n = 0 n = 1 n = 2 n = 3 n = 4 n = 5 constant 3 linear 5x + 4 quadratic.

Notes Over 6.8 Using x-Intercepts to Graph a Polynomial Function Graph the function. x-inter: 1, -2 End behavior: degree 3 L C: positive Bounces off of.

EXAMPLE 1 Use x-intercepts to graph a polynomial function

Polynomial Functions and Graphs. AAT-A IB - HR Date: 2/25/2014 ID Check Objective: SWBAT evaluate polynomial functions. Bell Ringer: Check Homework HW.

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

Warm-Up Exercises Multiply the polynomial. 1.(x + 2)(x + 3) ANSWER x 2 + 5x + 6 ANSWER 4x 2 – 1 2.(2x – 1)(2x + 1) 3. (x – 7) 2 ANSWER x 2 – 14x + 49.

The sum or difference of monomial functions. (Exponents are non-negative.) f(x) = a n x n + a n-1 x n-1 + … + a 0 Degree of the polynomial is the degree.

Section 5.2 – Polynomials, Linear Factors, and Zeros WHY??????????? A storage company needs to design a new storage box that has twice the volume of its.

Polynomial Functions and Models

Section 7.1 An Introduction to Polynomials. Terminology A monomial is numeral, a variable, or the product of a numeral and one or more values. Monomials.

Warm-up What is the standard form of a linear equation?

Finding Real Roots of Polynomial Equations 3-5

CC1 Key Features of a Graph Domain? Range? End-Behavior? Maximum? Minimum? Interval of Increase? Interval of Decrease?

Factor and Solve Polynomial Equations 2.3 (GREEN book)

5.2 Polynomials, Linear Factors, and Zeros

Polynomial Functions Remediation Notes.

Polynomials. DegreeNameExample 0Constant 1Linear 2Quadratic 3Cubic 4Quartic 5Quintic Some of the Special Names of the Polynomials of the first few degrees:

M3U4D10 Warm Up Write the equation in vertex form if the directrix is y = 10 and the focus is (3,4). y = -1/12 (x – 3) Collect Warmups Quiz.

Remainder Theorem Section 6-3b. Remainder Theorem.

8-1 A TTRIBUTES of Polynomial F UNCTIONS Objectives: To classify polynomials, graph polynomial functions, and describe end behavior. Classifying Polynomials.

Warm-Up Exercises EXAMPLE 1 Find a common monomial factor Factor the polynomial completely. a. x 3 + 2x 2 – 15x Factor common monomial. = x(x + 5)(x –

Polynomial Function Review

Warm Up Factor completely. 1. 2y3 + 4y2 – 30y 2y(y – 3)(y + 5)

Chapter 3: Polynomial Functions

Polynomial Functions and Graphs

Introduction to Polynomial Functions

Chapter 4: Rational Power, and Root Functions

Analyzing Graphs of Polynomial Functions

Choose the Best Regression Equation

Polynomial Functions and Graphs

Analyze graphs of Polynomial Functions Lesson 2.8

Polynomial Functions and Graphs

6.8 Analyzing Graphs of Polynomial Functions

Polynomials Dividing/ Factoring Equations Inequalities Miscel- laneous

An Intro to Polynomials

f (x) = anxn + an-1xn-1 +…+ a2x2 + a1x + a0

1. On your bingo card randomly number from 1 to 25.

ALGEBRA II HONORS/GIFTED - SECTION 5-1 (Polynomial Functions)

Warm-Up 4 minutes Evaluate each expression for x = -2. 1) -x + 1

6.4 Solving by Factoring.

Half Test Review! Day 6.

Polynomials, Linear Factors, and Zeros

Polynomial Functions and Graphs

Make sure you have book and working calculator EVERY day!!!

Polynomial Functions and Graphs

Presentation transcript:

SimplifyingRandomWord ProblemsSolvingProperties

Simplify then classify:

Quintic Polynomial of 4 terms

Simplify then classify:

Quartic Trinomial

Simplify then classify:

6 th degree polynomial of 5 terms

Divide then classify:

Quadratic Trinomial

Simplify then classify:

7 th degree polynomial of 5 terms

State the end behavior and number of turns of the function below.

End Behavior:  Number of Turns: 2

State the y- intercept and x- intercepts (including multiplicity) of the function

Y-intercept: (0.-4) X-intercept(s): (-2,0) Multiplicity of 3 (1,0) Multiplicity of 1

State the relative maxima, relative minima and range of the function

Relative Maxima: (-0.75, 9.5) Relative Minima: (2,0) Range: (-∞, ∞)

State the x- intercepts, relative maxima and relative minima

X-intercepts: (-3,0) (-2,0) (-1,0) (1,0) and (2,0) Relative Maxima: (-2.5,3) and (0,6) Relative Minima: (-1.5, -1.5) and (1.5,-5)

6 yd State the intervals of rising and falling

Interval of Rising: (-1.2, -0.5) U (0.5, 1.2) Interval of Falling: (-∞, -1.2) U (-0.5, 0.5) U (1.2, ∞)

Solve:

x = 0, x = -6 and x = 3

Solve:

. Solve:

Solve:

DAILY DOUBLE!!

Solve:

3 bridges

Cubic because it has a greater R 2 value.

There will be about 5,219 bacteria after 10 days.

A container has a length that is three times the width. The height of the box is 2 cm less than the length. Find the width of the box when the volume is 70 cm 3

2.2 cm

x x x x x xx x w l A piece of cardboard is cut into a box. The width of the original piece of cardboard is 10 inches and the length is 12 inches. Find the maximum volume of the box.

The maximum volume is in 3

4 Turns and 5 Solutions

(-.59, -1.8)

Determine a possible equation of a polynomial that has an x-intercept at 2 with a multiplicity of 2 and an x- intercept and -3 with a multiplicity of 1