Homework Check.

Slides:

Advertisements

Similar presentations

Essential Question: How do I analyze a polynomial function? Daily Questions: 1). How are turning points related to the degree of a polynomial? 2)How do.

Advertisements

7.1 and 7.2 Graphing Inequalities 7.3 Solving Equations Using Quadratic Techniques Algebra II w/ trig.

Polynomial Functions Zeros and Graphing Section 2-2.

The Graphs of Polynomials

Graphs of Polynomial Functions. Parent Graphs  Quadratic Cubic Important points: (0,0)(-1,-1),(0,0),(1,1)  QuarticQuintic  (0,0) (-1,-1),(0,0),(1,1)

Warm up The domain of a function is its a)y-values b) x-values c) intercepts  The range of a function is its a) y-values b) x-values c) intercepts.

Characteristics of Polynomials: Domain, Range, & Intercepts

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 =

Polynomials of Higher Degree 2-2. Polynomials and Their Graphs  Polynomials will always be continuous  Polynomials will always have smooth turns.

Warm Up Are the following graphs even or odd? (Draw them on your paper) 2.What are the zeros for the given polynomial function and what is the multiplicity.

Warm Up. Polynomial Graphs March 17 th & 18 th, 2014.

15.10 Graphing Polynomial Functions OBJ:  To sketch the graph of an integral polynomial function of degree n with n distinct roots.

1 What you will learn today…  How to use the Fundamental Theorem of Algebra to determine the number of zeros of a polynomial function  How to use your.

Determine the number and type of roots for a polynomial equation

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

Today in Calculus Derivatives Graphing Go over test Homework.

Polynomials Graphing and Solving. Standards MM3A1. Students will analyze graphs of polynomial functions of higher degree. a. Graph simple polynomial functions.

Lesson 2.2 Read: Pages Page 112: #1-9 (EOO), (EOO), (EOO)

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.

3.1 Polynomial Functions and their Graphs. f(x) = 3x 5 + 6x 4 – 2x 3 + 7x - 6.

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

LESSON 2–2 Polynomial Functions.

Objective: To determine the end behavior of polynomial functions

Polynomial Functions of Higher Degree

3.1 Polynomial Functions and their Graphs

Notes Over 3.4 The Rational Zero Test

Warmup 3-7(1) For 1-4 below, describe the end behavior of the function. -12x4 + 9x2 - 17x3 + 20x x4 + 38x5 + 29x2 - 12x3 Left: as x -,

4.3: Real Zeroes of Polynomials Functions

Pre-AP Algebra 2 Goal(s):

2.1 Day 2 Homework Answers D: −2,∞

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

Bell ringer Simplify the following expressions as much as you can!

4.2 Properties of Polynomial Graphs

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

Graphing Polynomial Functions

Polynomial Functions f(x) = a f(x) = ax + b f(x) = ax2 + bx + c

Polynomial Functions and Models

Polynomial Functions of Higher Degree

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.

Evaluate and Graph Polynomial Functions

Graphing Polynomials Unit 1D Day 19.

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

Polynomial Functions and Their Graphs

Lesson 5.8 Graphing Polynomials.

Functions AII.7 cdf 2009.

Which of the following are polynomial functions?

Solve the inequality and graph the solution set on the number line

End Behaviors Number of Turns

I can write the equation of a

7.2 Graphing Polynomial Functions

4.3 - End Behavior and Graphing

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:

Students, Take out your calendar and your homework

Polynomial Functions 1 Definitions 2 Degrees 3 Graphing.

2. What “test” can you use to determine if a graph is a function?

DO NOW 5/12/15 Identify the degree and leading coefficient of the following polynomials y = 3x3 – 2x + 7 y = -x4 + 3x2 – x + 8 y = 2x2 – 7x y = -x7 + x4.

Homework Check.

Section 2.3: End Behavior of Polynomial Functions

End Behavior, Extrema & Sketching

Multiply each expression.

Preview to 6.7: Graphs of Polynomial

MATH 1310 Section 4.1.

Polynomial Functions of Higher Degree

5.3 Polynomial Functions.

Bellwork Solve the Polynomial Equation by Factoring

Polynomial Functions of Higher Degree

Presentation transcript:

Homework Check

End Behavior, Extrema & Sketching

End Behavior right up or down up or down leftt Look left and right, to figure out what’s happening up and down. right up or down up or down leftt

End Behavior: From a Graph 1. 2. 2.

End Behavior: From a Graph 3. 3. 4.

5. f(x) = x4 + 2x2 – 3x 6. f(x) = -x5 +3x4 – x 7. f(x) = 2x2 + 3x3 + 5 Determine the left and right behavior based on the equation. 5. f(x) = x4 + 2x2 – 3x 6. f(x) = -x5 +3x4 – x 7. f(x) = 2x2 + 3x3 + 5

Tell me what you know about the equation… Odd degree Positive leading coefficient

Tell me what you know about the equation… Page 261 #53 Even degree Negative leading coefficient

Tell me what you know about the equation… Page 261 #54 Odd degree Positive leading coefficient

Extrema are turns in the graph. If you are given a graph take the turns and add 1 to get the least possible degree of the polynomial. If you are given the function, take the degree and subtract 1 to get the extrema. f(x) = 2x3 – 3x2 + 5 3rd degree, 2 extrema 4th degree, 3 extrema

8. What is the least possible degree of this function?

9. What is the least possible degree of this function?

What if you didn’t have a graph? 10. f(x) = x4 + 2x2 – 3x Number of Extrema: ____ 11. f(x) = -x5 +3x4 – x Number of Extrema: ____ 12. f(x) = 2x3 – 3x2 + 5 Number of Extrema: ____

Sketching: # of Zeros: _________ Y-Int: ________ 1

Sketching: # of Zeros: _________ Y-Int: ________

Homework: Worksheet ALL