Mathematical Analysis

Slides:

Advertisements

Similar presentations

Polynomial Inequalities in One Variable

Advertisements

2.4 – Zeros of Polynomial Functions

Approximating Zeroes Learning Objective: to be able to find all critical points of a polynomial function. Warm-up (IN) Describe the graph: 1. 2.

Notes Over 6.7 Finding the Number of Solutions or Zeros

2.3 Synthetic Substitution

6.3 – Evaluating Polynomials. degree (of a monomial) 5x 2 y 3 degree =

2.3 Synthetic Substitution OBJ:  To evaluate a polynomial for given values of its variables using synthetic substitution.

Class Work Find the real zeros by factoring. P(x) = x4 – 2x3 – 8x + 16

9/24 Warm Up 1) If (-5,-3) is a point on an odd function, name another point on the function. What if f was an even function? 2) For the following function:

DO NOW: Take out your Review HW & begin the Do Now!!!

Sec 3.1 Polynomials and Their Graphs (std MA 6.0) Objectives: To determine left and right end behavior of a polynomial. To find the zeros of a polynomial.

Algebra 2/TrigonometryName: __________________________ 6.6 WorksheetDate: ________________ Block: _____ For each polynomial, complete the following: (a)

Help the Poor Math Student  Vocabulary Dividend: number being divided Divisor: number you are dividing by Quotient: is number you get when you divide.

5.2 Polynomials, Linear Factors, and Zeros P

Graphing Polynomials Without a Calculator Objective: You should be able to graph polynomial functions (including their changes) without a calculator.

4.4 The Rational Root Theorem

5.6 The Fundamental Theorem of Algebra. If P(x) is a polynomial of degree n where n > 1, then P(x) = 0 has exactly n roots, including multiple and complex.

Specialist Mathematics Polynomials Week 3. Graphs of Cubic Polynomials.

5.2 Polynomials, Linear Factors, and Zeros

Objective: Students will be able to graph rational functions using their asymptotes and zeros.

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.

Objective: SWBAT understand and apply the Fundamental Theorem of Algebra and the Linear Factorization Theorem to find a polynomial given real and complex.

Warm-Up 2/26 1. J. Rigor: You will learn how to find the real and complex zeros of polynomial functions. Relevance: You will be able to use graphs and.

Polynomial P(x) Linear Factors Solutions of P(x)=0 Zeros of P(x) P(x) = 0.

3.2 Division of Polynomials. Remember this? Synthetic Division 1. The divisor must be a binomial. 2. The divisor must be linear (degree = 1) 3. The.

8.2 The Reciprocal Function Family Honors. The Reciprocal Functions The Reciprocal function f(x) = x ≠0 D: {x|x ≠ 0} R: {y|y ≠ 0} Va: x = 0 Ha: y = 0.

Section 3.2 Dividing Polynomials (std Alg 2 3.0)

The Real Roots of Polynomials

Solving Higher Degree Polynomial Equations.

Algebra II 5.6: Find Rational Zeros HW tonight: p.374 (4-10 even)

7.3 Products and Factors of Polynomials

8-6 Solving Polynomial equations in factored form

Linear Inequalities in Two Variables

6.3 Dividing Polynomials.

February 29, 2012 Happy Leap Year

5.2/5.9 Polynomial & Linear Factors

Algebra II Elements 5.8: Analyze Graphs of Polynomial Functions

Conjugates & Absolute Value & 14

Section 6.3 Dividing Polynomials

Polynomial Inequalities in One Variable

Take your H.W. and leave on desk. Complete “DO NOW”

Students will be able to calculate and interpret inverse variation.

Warm Up Test Friday HW- Solving Quadratics Worksheet.

1. Use the quadratic formula to find all real zeros of the second-degree polynomial

Functions and Inverses

Warm-up: Find the equation of a quadratic function in standard form that has a root of 2 + 3i and passes through the point (2, -27). Answer: f(x) = -3x2.

LEARNING GOALS – LESSON 6.4

Fundamental Theorem of Algebra

Solving Equations in Factored Form

Day 9 – Graphing Polynomial Functions by Hand

A graphing calculator is required for some problems or parts of problems 2000.

EXIT TICKET: Graphing Linear Equations 11/17/2016

Objectives Use the Factor Theorem to determine factors of a polynomial. Factor the sum and difference of two cubes.

The Factor Theorem A polynomial f(x) has a factor (x − k) if and only if f(k) = 0.

Unit 1 – Linear Programming

Real Zeros of Polynomial Functions

3.6 Polynomial Functions Part 2

7.1 solving linear systems by graphing

Review Write the product of the sum and difference. (x + 3) (x – 3)

Welcome: Pass out Zeros of Higher Polynomials WKS.

Section 6.6 Day 1 Solving Systems of Inequalities

Warm-up: State the domain.

Bell Ringer In elementary school, you learned long division. Describe, in detail, how to divide 230 by 4 without a calculator.

Preview to 6.7: Graphs of Polynomial

1.) 2.) Algebra 2/Trigonometry Name: __________________________

Objective SWBAT solve polynomial equations in factored form.

Divide using long division

M3D17 Have out: Bellwork: pencil, red pen, highlighter, GP notebook

U7D13 Have out: Bellwork: pencil, red pen, highlighter, GP notebook

Presentation transcript:

Mathematical Analysis Finding the Zeros of a Function

Objectives & HW: Students will be able to and use the given zero to completely factor a function into linear factors. HW: p. 235: 66-70 even

Ex 1. Given that P(x)= , and given that is a zero, factor the polynomial. Graph the polynomial first by hand and check using a calculator.

Ex 2. Given is a zero, completely factor .

You Try! Completely factor: 1. One zero is 2.

Exit Ticket!