Choose the Best Regression Equation

Slides:

Advertisements

Similar presentations

Lesson 2-4 Finding Maximums and Minimums of Polynomial Functions.

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.

Pg. 98/110 Homework Pg. 127#25 – 28 all Pg. 138#42, 43, 48, 88 – 93 all #58 15 liters of 20% acid and 10 liters of 35% acid # liters of distilled.

Pre – CalcLesson 2.4 Finding Maximums and Minimums of Polynomial Functions For quadratic functions: f(x) = ax 2 + bx + c To fin d the max. or min. 1 st.

Applications of Cubic Functions

Choose the Best Regression Equation

A rectangular dog pen is constructed using a barn wall as one side and 60m of fencing for the other three sides. Find the dimensions of the pen that.

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

Investigating Graphs of Polynomial Functions 6-7

Example 2 Finding the Maximum Volume Chapter 6.3 A box is to be formed by cutting squares x inches per side from each corner of a square piece of cardboard.

4.4 Optimization Finding Optimum Values. A Classic Problem You have 40 feet of fence to enclose a rectangular garden. What is the maximum area that you.

2.8 Analyzing Graphs of Polynomial Functions p. 373

2.8 Analyze Graphs of Polynomial Functions

Pg. 116 Homework Pg. 117#44 – 51 Pg. 139#78 – 86 #20 (-2, 1)#21[0, 3] #22 (-∞, 2]U[3, ∞)#24(-∞, -3]U[½, ∞) #25 (0, 1)#26(-∞, -3]U(1, ∞) #27 [-2, 0]U[4,

SimplifyingRandomWord ProblemsSolvingProperties.

Objectives Use properties of end behavior to analyze, describe, and graph polynomial functions. Identify and use maxima and minima of polynomial functions.

Let’s start with a problem today…Using only algebra, find

Polynomial Functions and Models Section 5.1. Polynomial Functions.

1. find. 2. Find the domain of D: All real numbers.

Pre-AP Pre-Calculus Chapter 2, Section 3

Investigating Graphs of Polynomial Functions 6-7

MAT 150 – CLASS #21 Topics: Model and apply data with cubic and quartic functions Solve Polynomial Equations Find factors, zero, x-intercepts, and solutions.

2.7 Quiz (on a separate paper) No Calculator Please 1) For the function find: a)Vertical Asymptotes and holes b) Horizontal (or) Slant Asymptotes c) X-intercepts.

Copyright © 2014, 2010, 2006 Pearson Education, Inc. 1 Chapter 3 Quadratic Functions and Equations.

PRE-ALGEBRA. Reasoning Strategy: Make a Model (10-8) How can you use a model to help solve a problem? Example: A box company makes boxes to hold popcorn.

6.8 Analyzing Graphs of Polynomial Functions

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

Sullivan PreCalculus Section 2.6 Mathematical Models: Constructing Functions Objectives Construct and analyze functions.

Quadratic Formula and Applications. The Quadratic Formula The following nine slides contain videos with music to help you memorize the quadratic formula.

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

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

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 Behavior patterns in the graphs. Warm Up List and name the transformations in this diagram.

Polynomial Functions and Models

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

Matt 6-7 pm Week 6, Session 2 MATH 1300 SI. Sundays: 7:05-8:05 Mondays: 6:00-7:00 Wednesdays: 6:00-7:00 Morton MATH 1300 SI.

Jeopardy Math II Ms. Brown’s 2 nd Period Class. Quadratics Factoring Square Roots Quadratic Formula Graphically Word Problems FINAL.

Applied Max and Min Problems (Optimization) 5.5. Procedures for Solving Applied Max and Min Problems 1.Draw and Label a Picture 2.Find a formula for the.

3.3B Solving Problems Involving Polynomials

Objectives: Students will be able to… Determine the number of zeros of a polynomial function Find ALL solutions to a polynomial function Write a polynomial.

5.2 Polynomials, Linear Factors, and Zeros

Make a Model A box company makes boxes to hold popcorn. Each box is made by cutting the square corners out of a rectangular sheet of cardboard. The rectangle.

Building Boxes What is the largest volume open top box that you can build from an 8 ½ by 11 inch sheet of paper?

5-4 Day 1 modeling & optimization

Chapter 4: Rational Power, and Root Functions

Analyzing Graphs of Polynomial Functions

Polynomial Functions of Higher Degree with Modeling

1-6 Modeling with functions

Bellwork You are making a rectangular box out of a 16-inch-by-20- inch piece of cardboard. The box will be formed by making the cuts shown in the diagram.

Analyze graphs of Polynomial Functions Lesson 2.8

6.8 Analyzing Graphs of Polynomial Functions

Objectives Use properties of end behavior to analyze, describe, and graph polynomial functions. Identify and use maxima and minima of polynomial functions.

Objectives Use properties of end behavior to analyze, describe, and graph polynomial functions. Identify and use maxima and minima of polynomial functions.

3.6 Mathematical Models: Constructing Functions

7.3 Integral & Rational Zeros of Polynomial Functions

2.7 Mathematical Models: Constructing Functions

Chapters 1 & 2 Review Day.

Polynomials: Application

Objectives Use properties of end behavior to analyze, describe, and graph polynomial functions. Identify and use maxima and minima of polynomial functions.

Quadratic Applications

Warm Up Identify all the real roots of each equation.

Chapter 3: Polynomial Functions

Objectives Use properties of end behavior to analyze, describe, and graph polynomial functions. Identify and use maxima and minima of polynomial functions.

2.7 Mathematical Models: Constructing Functions

6.7 Using the Fundamental Theorem of Algebra

Solving Quadratic Equations by Finding Square Roots

Optimization (Max/Min)

Finding Maximums & Minimums of Polynomial Functions fguilbert.

Presentation transcript:

Choose the Best Regression Equation Notes Day 6.5 Choose the Best Regression Equation Volume of a Box cubic Application Problems

Complete a regression equation to find the best model. Go to “catalog” on the calculator and turn “diagnostics on.” x Y -5 -842 -1 -6 8 2 12 4 184 5 408 Quadratic: R2= .9304 Y = -9.326x2 + 109.571x – 20.288 Cubic: R2= 1 Y = 5x3 – 9x2 – (2.4• 10-11)x + 8 Quartic: R2= 1 but not really quartic Y = (5.57• 10-12)x4 + 5x3 – 9x2 + 8 Cubic Regression is best

Cuts of 1.811 inches will maximize volume to 96.771 cubic inches An open box is to be made from a 10-in. by 12-in. piece of cardboard by cutting x-inch squares in each corner and then folding up the sides. Write a function giving the volume of the box in terms of x. Approximate the value of x that produces the greatest volume. A. Label the side lengths in terms of x 12 – 2x Write an equation in factored form for the volume as if the box were closed. x x V(x)=(12 – 2x)(10 – 2x)(x) 10 – 2x C. Find the roots and plot on the graph. X = {6,5,0} Write the volume equation in standard form and plot the end behavior on the graph. V(x)=(120 – 44x + 4x2)(x) V(x)=4x3 – 44x2 + 120x 90 E. Find the relative min/max on the calculator. Plot. (1.811 , 96.771) Min(5.523 , - 5.511) F. Explain what this ordered pair represents? 5 Cuts of 1.811 inches will maximize volume to 96.771 cubic inches Why isn’t volume greatest as x approaches infinity? Some dimensions would be negative. G. What are the dimensions of the box? 8.378 in. by 6.378 in. by 1.811 in.