Solving Quadratic Equations – Comparing and Contrasting Methods April 21, 2015.

Slides:



Advertisements
Similar presentations
Unit 4 Lesson 4: Solving Polynomial Equations State StandardsLesson Goals 3: Add, subtract, multiply and divide (including long division) polynomials.
Advertisements

Today’s quiz on 8.2 B Graphing Worksheet 2 will be given at the end of class. You will have 12 minutes to complete this quiz, which will consist of one.
Bell Problem Perform the indicated operation. (x -5)(x2 – 5x + 7)
Many quadratic equations can not be solved by factoring. Other techniques are required to solve them. 7.1 – Completing the Square x 2 = 20 5x =
7.1 – Completing the Square
+ Completing the Square. + In your notes: Simplify the following: (5 – 3i)(4 + 2i) 3.
10.7 Factoring Special Products
Make sure you know the day and time of the final exam for this section of Math 110: Day: ______ Date:______ Time: ______ to _______ All Math 110 finals.
Please close your laptops and turn off and put away your cell phones, and get out your note-taking materials. Today’s daily homework quiz will be given.
6 – 4: Factoring and Solving Polynomial Equations (Day 1)
Coming up in Math 110: Today: Review for Quiz 4. Tomorrow: Quiz 4 on sections & 8.2 Thursday: Review for Test 2 Next Monday: Test 2 on all of.
Algebra: Wednesday’s Daily Inspiration Factor the following quadratic equations AND then identify the roots: 1.y = -2x x y = -x 2 + 8x – 16.
Math 110: Precalc 11 When you first arrive in class: –If you have any questions about the homework please put the question #’s on the board If someone.
Do Now: Pass out calculators. 1. Compare and contrast factoring: 6x 2 – x – 2 with factoring x 2 – x – 2 Factor both of the problems above. Write a few.
Please close your laptops and turn off and put away your cell phones, and get out your note-taking materials.
Factor Special Products April 4, 2014 Pages
Perfect Square Trinomials and Difference of Perfect Squares
Factoring Special Products
Multiplication and Division Basic Facts
Factoring and Solving Polynomial Equations Chapter 6.4.
Solving Quadratics. Methods for Solving Quadratics Graphing Factoring Square Root Method Completing the Square Quadratic Formula.
Completing the Square 4-6 Day 1 Today’s Objective: I can use the process of completing the square to solve or rewrite a quadratic equation.
Objective: 6.4 Factoring and Solving Polynomial Equations 1 5 Minute Check  Simplify the expression
EXAMPLE 3 Factor by grouping Factor the polynomial x 3 – 3x 2 – 16x + 48 completely. x 3 – 3x 2 – 16x + 48 Factor by grouping. = (x 2 – 16)(x – 3) Distributive.
Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring.
Chapter 10.7 Notes: Solve Quadratic Equations by the Quadratic Formula Goal: You will solve quadratic equations by using the Quadratic Formula.
Do Now : Evaluate when x = 6, y = -2 and z = The Quadratic Formula and the Discriminant Objectives Students will be able to: 1)Solve quadratic.
Learning Task/Big Idea: Students will learn how to find roots(x-intercepts) of a quadratic function and use the roots to graph the parabola.
New Unit on Factoring, Quadratic Equations, & Quadratic Functions SWBAT… 1. Factor polynomials using the distributive property 2. Factor a trinomial in.
Bell Work Solve the Equation by Factoring or using Square Roots: Solve the equation by using the quadratic formula: 3. Identify the parts of a parabola:
Section 6.4 Solving Polynomial Equations Obj: to solve polynomial equations.
Solving Polynomial Equations
6.4 Solving Polynomial Equations. One of the topics in this section is finding the cube or cube root of a number. A cubed number is the solution when.
Solve by factoring. x² = - 4 – 5x 2,. Solve by factoring. n² = -30 – 11n -4 and -1.
GOAL: FACTOR CUBIC POLYNOMIALS AND SOLVE CUBIC EQUATIONS Section 6-5: Factoring Cubic Polynomials.
©thevisualclassroom.com To solve equations of degree 2, we can use factoring or use the quadratic formula. For equations of higher degree, we can use the.
Warm - up Factor: 1. 4x 2 – 24x4x(x – 6) 2. 2x x – 21 (2x – 3)(x + 7) 3. 4x 2 – 36x + 81 (2x – 9) 2 Solve: 4. x x + 25 = 0x = x 2 +
Flipping the classroom FOUNDATIONS OF ALGEBRA 2 / TRIG.
Q3.W4 Math – Monday– 1/26/15 Today:  Warm-up  Correct 7.1 and 7.2 Quizzes  Quiz Corrections Due by Monday 2/2/15  7.3 Equations with the Distributive.
Completing the Square SPI Solve quadratic equations and systems, and determine roots of a higher order polynomial.
Section 5-5: Factoring Using Special Patterns Goal: Factor Using Special Patterns.
Warm Up. 4.3 Solve by Factoring Find this in your notes!
Quiz 2 Feedback & Factoring Monday, September 16 Make sense of problems and persevere in solving them.
Section )by graphing (using the calculator to identify the roots (x-intercepts)) 2)by factoring 3)by “completing the square” 4)by Quadratic Formula:
Date: 8/23/11- Section: Prerequisites P.4 pg Objective: SWBAT write the equation of perpendicular and parallel lines in real world applications.
Algebra 2 Notes March 23, Do you remember the Quadratic Formula? - Work with the people around you. Brainstorm and try and remember the quadratic.
Algebra II Please take out last night’s homework assignment 3-66, 3-68, 3-69 Please record tonight’s homework on your pink assignment chart Study for quiz.
Algebra 2 Monday Warm-Ups Check in and discuss A#6.5 Discussion/Notes/Guided Practice Section 6.6 Solving Polynomial Equations Assignment A#6.6.
Do Now: Solve x2 – 20x + 51 = 0 3x2 – 5x – 2 = 0 Today’s Agenda
Solving Quadratics Algebra 2 Chapter 3 Algebra 2 Chapter 3.
Notes Over 10.7 Factoring Special Products Difference of Two Squares.
Tuesday, June 4, 2013 Do Now : Evaluate when x = 6, y = -2 and z = 3.
Math 110: Precalc 11 When you first arrive in class: –If you have any questions about the homework please put the question #’s on the board If someone.
Warm Up. 4.6 Quadratic Formula What THREE methods have we used so far to solve quadratics? Today you will learn the 4 th and LAST method used for solving.
Warm Ups Term 2 Week 6.
AIM #1.5: How do we solve quadratic equations?
Warm - up x2 – 24x 4x(x – 6) 2. 2x2 + 11x – 21 (2x – 3)(x + 7)
Solving Quadratic Equations by the Complete the Square Method
Review of Factoring; Quadratic Equations and Rational
Solving Quadratic Equations
Warm Up Solve each of the quadratic functions: x2 – 3 = 0
Warm Up Test Friday HW- Solving Quadratics Worksheet.
Lesson 9.7 Factor Special Products
Opener Perform the indicated operation.
5.4 Factor and Solve Polynomial Equations
Factor & Solve Polynomial Equations
Objective - To solve quadratic equations by completing the square.
Quadratic Equations.
Warm-up  .
L5-7 Objective: Students will be able to solve quadratics by using the quadratic formula.
Presentation transcript:

Solving Quadratic Equations – Comparing and Contrasting Methods April 21, 2015

After looking at your practice quizzes, here are the biggest misconceptions that I noticed:

There are 5 methods that you have learned for solving quadratic equations: Factoring Completing the Square Graphing Taking the Square Root The Quadratic Formula

Factoring a = 1 Factor normally or use British Method

Solving Quadratic Equations: Factoring

Completing the Square a = 1 Complete the Square using normal process

Solving Quadratic Equations: Completing the Square

Solving Quadratic Equations: Graphing

Solving Quadratic Equations: The Quadratic Formula

Solving Quadratic Equations: Taking the Square Root

It’s often going to be up to you to solve to choose a method for solving quadratic equations, especially on a college admissions test. What’s your plan if you try one method and it doesn’t work? How can you know for sure how many solutions a quadratic equation has? What, in your opinion, is the best method for solving quadratic equations?

Explain the difference between a quadratic equation, quadratic function, and the quadratic formula.

Up next this week and next week: Today: Factoring by Completing the Square (cont’d) and Deriving the Quadratic Formula Tomorrow: Factoring by Guess-and-Check and Review Difference of Squares/Perfect Square Trinomials Thursday: Factoring Word Problems Friday: Factoring by Grouping and Distributive Property and More Word Problems Monday: Rotated Out Tuesday: Review Day Wednesday: Unit Test – Factoring, Solving Quadratic Equations, and Polynomials

Team Challenge: Complete the Square on the General Case For this group challenge, you and your team will attempt to complete the square on the general case of a quadratic equation The specifics: The first 4 minutes are independent work time so that you can gather ideas, brainstorm a strategy, and prepare to work with your group. You will then have 7 minutes to complete the square with your group The Prize: Any group demonstrating their complete process and correctly completing the square will earn a homework pass for tonight, Wednesday, April 23 rd

Factoring by (Grouping) April 22, 2015

This topic should be familiar – you have already factored by grouping with the British Method!

Sum and Difference of Cubes Patterns Two other special factoring patterns!

Helpful memory trick:

Small-Group Work: Please complete today’s worksheet with your group.