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

Slides:

Advertisements

Similar presentations

Polynomial Functions Zeros and Graphing Section 2-2.

Advertisements

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.

Real Zeros of Polynomial Functions 2-3. Descarte’s Rule of Signs Suppose that f(x) is a polynomial and the constant term is not zero ◦The number of positive.

Pg. 222 Homework Pg. 223#31 – 43 odd Pg. 224#48 Pg. 234#1 #1(-∞,-1)U(-1, 2)U(2, ∞) #3 (-∞,-3)U(-3, 1)U(1, ∞) #5(-∞,-1)U(-1, 1)U(1, ∞) #7(-∞, 2 – √5)U(2.

7.4 and 7.5 Solving and Zeros of Polynomials

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

1. Describe the end behavior of the graph y = 2x 5 – 3x Sketch a graph of 3 rd degree with a zero at -5 (multiplicity 2) and a zero at 0 (multiplicity.

FACTOR to SOLVE 1. X 2 – 4x X 2 – 17x + 52 (x-10)(x + 6) x = 10, -6 (x-4)(x - 13) x = 4,13.

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

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 =

Pg. 223/224/234 Homework Pg. 235 #3 – 15 odd Pg. 236#65 #31 y = 3; x = -2 #33y = 2; x = 3 #35 y = 1; x = -4#37f(x) → 0 #39 g(x) → 4 #41 D:(-∞, 1)U(1, ∞);

Using Multiplicity and Graphs to Determine Equations 8 November 2010.

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

Do Now: Match each polynomial function with its graph. Explain your reasoning. Use a graphing calculator to verify your answers. 1. f (x) = x 3 − x 2.

2.1 Linear and Quadratic Functions and Modeling Objective: Students will be able to identify specific types of functions, describe properties of those.

Section 3.2 Polynomial Functions and Their Graphs

LESSON 2–2 Polynomial Functions.

Today in Pre-Calculus Need a calculator Review Chapter 2 Homework.

Notes 4.3 Graphs of Polynomial Functions

2.2(b) Notes: Polynomial Functions of Higher Degree

Real Zeros of Polynomial Functions

Warm Up: Solve & Sketch the graph:

Mod. 3 Day 4 Graphs of Functions.

2.1 Day 2 Homework Answers D: −2,∞

MCS 118 Fall 2013 September 16, 2013.

Smooth, Continuous Graphs

Pre-Calculus Section 2.2 Polynomial Functions of Higher Degree

Section 3.2 Polynomial Functions and Their Graphs

Polynomial Functions and Modeling

Graphing Polynomial Functions

Finding the Zeros of a Polynomial Function

Graphs of Polynomial Functions

Polynomial Functions Defn: Polynomial function

Polynomial Multiplicity

Warm-up: Sketch the graph of f(x) = x5 – 4x4 + 4x3. Be sure to include all critical values. HW: Quiz Review 2.1/2.2.

Finding the Zeros of a Polynomial Function

Graphing Polynomials Unit 1D Day 19.

7.4 and 7.5 Solving and Zeros of Polynomials

Graph Polynomials Effect of Multiplicity on a graph

Finding the Zeros of a Polynomial Function

Polynomial Functions and Their Graphs

Functions AII.7 cdf 2009.

Section 2.3 Polynomial Functions and Their Graphs

End Behaviors Number of Turns

7.2 Graphing Polynomial Functions

Section 3.2 Polynomial Functions and Their Graphs

4.3 - End Behavior and Graphing

Polynomial Functions of Higher Degree

Bell Ringer What is a function?

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:

4.3: Polynomial Functions

Graph Polynomials Effect of Multiplicity on a graph

Pre-Calculus Go over homework End behavior of a graph

Polynomial Functions of Higher Degree

Finding the Zeros of a Polynomial Function

“Why so serious?”.

Graphs of Polynomial Functions

Homework Check.

2.6 Find Rational Zeros Pg. 89.

6-8 Roots and Zeros Given a polynomial function f(x), the following are all equivalent: c is a zero of the polynomial function f(x). x – c is a factor.

Graphs of Polynomial Functions

Section 2.3: End Behavior of Polynomial Functions

2.6 Find Rational Zeros Pg. 89.

5.3 Polynomial Functions.

Today in Pre-Calculus Go over homework.

Bellwork Solve the Polynomial Equation by Factoring

Pre-AP Pre-Calculus Chapter 2, Section 5

Polynomial Functions of Higher Degree

Presentation transcript:

Today in Pre-Calculus Go over homework Notes: (need calculator & book) Graphs of Polynomial Functions End Behavior Zeros Homework

End Behavior of Polynomial Functions Page 203 Exploration 1 If degree of polynomial is odd If degree of polynomial is even If leading coefficient is negative: graph reflects over x-axis so the end behavior changes signs.

End Behavior of Polynomial Functions Examples: Describe the end behavior of the following functions without graphing them. 1) f(x) = x3 + 2x2 – 11x – 12 2) g(x) =–2x4 + 2x3 – 22x2 – 18x + 35

Finding Zeros of Polynomial Functions Example: Find the zeros of f(x) = 5x3 – 5x2 – 30x 5x3 – 5x2 – 30x = 0 set equal to zero 5x(x2 – x – 6) = 0 factor GCF 5x(x – 3)(x + 2) = 0 factor 5x = 0 x – 3 = 0 x + 2 = 0 set EVERY term = 0 x = 0, 3, -2 solve for x

Multiplicity of a Zero If f is a polynomial function and (x – c)m is a factor of f, then c is a zero of multiplicity m. (c is a repeated zero). Example: f(x) = (x – 2)3(x+1)2 If the multiplicity is odd, then the graph crosses the x-axis at (c,0) and the value of f changes sign at x = c If the multiplicity is even, then the graph touches (but does not cross) the x-axis at (c,0) and the value of f does NOT change sign at x = c

Homework Pg. 209: 9-12, 26-28, 34, 36, 39-41 Quiz: Tuesday, October 30