Warm-up: HW: Cumulative Review Packet

Slides:

Advertisements

Similar presentations

4.4 Rational Root Theorem.

Advertisements

$100 $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 $200 $300.

Rational Functions Characteristics. What do you know about the polynomial f(x) = x + 1?

3.3 Zeros of polynomial functions

Descartes’s Rule of Signs & Bounds: Things that make your life easier TS: Making decisions after reflection and review.

2.5 Zeros of Polynomial Functions

2.5 Descartes’ Rule of Signs To apply theorems about the zeros of polynomial functions To approximate zeros of polynomial functions.

2.5 Real Zeros of Polynomial Functions Descartes Rule of Signs

2.3E- Descartes Rule of Signs Descartes Rule of Signs: Used to limit the number of choices in your list of POSSIBLE rational zeros. (helpful if you don’t.

Warm-up Find all the solutions over the complex numbers for this polynomial: f(x) = x4 – 2x3 + 5x2 – 8x + 4.

Problem of the day Can you get sum of 99 by using all numbers (0-9) and only one mathematical symbols ?

Section 2.5 Part Two Other Tests for Zeros Descartes’s Rule of Signs Upper and Lower Bounds.

2 pt 3 pt 4 pt 5pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2pt 3 pt 4pt 5 pt 1pt 2pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4pt 5 pt 1pt Roly Poly Divide and Conquer! Get.

Splash Screen. Example 1 Identify Possible Zeros A. List all of the possible rational zeros of f(x) = 3x 4 – x Answer:

POLYNOMIAL, RATIONAL, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS College Algebra.

Section 4.3 Zeros of Polynomials. Approximate the Zeros.

Real Zeros of Polynomial Functions. Quick Review.

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.

Do Now: Find all real zeros of the function.

Chapter 3 – Polynomial and Rational Functions Real Zeros of Polynomials.

Zeros of Polynomials 2.5.

2.4/2.52.4/2.5 Real Zeros of Polynomial Functions.

The Real Zeros of a Polynomial Function Obj: Apply Factor Theorem, Use Rational Zero Theorem to list roots, Apply Descartes’ Rule of Signs to determine.

Chapter 4: Polynomial and Rational Functions. Warm Up: List the possible rational roots of the equation. g(x) = 3x x 3 – 7x 2 – 64x – The.

Chapter 4: Polynomial and Rational Functions. Determine the roots of the polynomial 4-4 The Rational Root Theorem x 2 + 2x – 8 = 0.

Warm Up 9/2. Homework Questions Announcements Quiz Friday HW 2.4 pg. 206 #’s even, even.

Real Zeros of Polynomial Functions. Solve x 3 – 2x + 1 = 0. How? Can you factor this? Can you use the quadratic formula? Now what if I tell you that one.

Precalculus Lesson 2.5 The Fundamental Theorem of Algebra.

Warm – up #5. Homework Log Fri 1/8 Lesson 5 – 4 Learning Objective: To apply Rational Zeros Theorem Hw: #507 Pg. 302 #1 – 19 odd.

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

Warm – up #6 1 3 –2 – – – – 1 3–5–16 – 23– 8– 5 – 3 3– 1112 –21 3 is upper bound – 3 is lower bound Stop when neg. Stop when.

TRASHKETBALL PRECALCULUS CHAPTER 2 QUIZ. WHAT IS THE VERTEX AND WHAT ARE THE INTERCEPTS?

2.5 Zeros of Polynomial Functions Question to be answered: How do we determine zeros of functions that we cannot factor easily? Copyright © by Houghton.

3.3 Real Zeros of Polynomials. Rational Zero Theorem If the polynomial P(x) has integer coefficients then every rational zero of P is of the form p/q.

Pre-Calculus/Trig Name: __________________________ Unit 2 ReviewDate: _______________ Block: ______ Directions: Complete all work on a separate piece of.

5.6 More Graphs of Polynomial Functions

Warm Up Compute the following by using long division.

HOMEWORK CHECK.

Descartes’ Rule of Signs

Roly Poly Divide and Conquer! Get to the root of the Problem!

College Algebra Chapter 3 Polynomial and Rational Functions

Descartes Rule of Signs Positive real zeros = Negative real zeros =

Notes Over 3.4 The Rational Zero Test

Review Chapter 2 Sections

3.3 Real Zeros of Polynomials

4.2 Real Zeros Finding the real zeros of a polynomial f(x) is the same as solving the related polynomial equation, f(x) = 0. Zero, solution, root.

5.4 Finding All Zeros of a Polynomial

2.2(a) Notes: Polynomial Functions of Higher Degree

The Fundamental Theorem of Algebra (Section 2-5)

Warm-up: Given the function f(x) = 6x4 – 7x3 – 10x2

Warm Up Graph the following y= x4 (x + 3)2 (x – 4)5 (x – 3)

**Get signed by your parents for 5 bonus points on the test!!

WARM UP Find all real zeros of the functions

The Rational Zero Theorem

Zeros of a Polynomial Function Shortcuts?

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.

Warm Up Graph the following y= x4 (x + 3)2 (x – 4)5 (x – 3)

Real Zeros of Polynomial Functions

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:

Warm-up: Find f(2) for HW: pg. 248(2 – 14even, 18, 20, 26, 31, 46, 48)

Warm-up: CW: Cumulative Review 5 F(x) = 2x3 + 3x2 – 11x – 6

Zeros of polynomial functions

Section 2.4: Real Zeros of Polynomial Functions

Find all the real zeros of the functions.

In all the problems do the following:

5.3 Polynomial Functions.

Lesson #1 Introduction and Sections 3.1 & 3.2

Presentation transcript:

Warm-up: HW: Cumulative Review Packet Describe the left and right hand behavior Determine the range of the function Use Descartes Rule to find the possible number of + or – real zeros Use the Rational Zeros Test to determine the possible real zeros Write f(x) in factored form Find all the real zeros of f(x) Find the y-intercept. Is x = -1 an upper bound, lower bound, or neither? HW: Cumulative Review Packet

HW Answers: pg. 248(2 – 14even, 18, 20, 26, 31, 46, 48)

The Real Zeros of a Polynomial Function Objective: Use Descartes Rule of Signs Use the Rational Zeros Test Find bounds for real zeros of polynomial functions Factor polynomials completely Find real zeros of a polynomial

HW: Cumulative Review Packet Sneedlegrit: Find all rational zeros: HW: Cumulative Review Packet