SlideShare a Scribd company logo
4.5 QUADRATIC EQUATIONS
Solving by Factoring
DEFINTIONS
 The y – intercept is the point(s) where the graph
  touches or crosses the y – axis
 The x – intercept is the point(s) where the graph
  touches or crosses the x – axis
       The x – intercepts are also called the zero(s) of the
        function
ZERO-PRODUCT PROPERTY
   The zero – product property can be used to solve
    some quadratic equations in standard form.

    The Zero – Product Property
    If ab = 0, then a = 0 or b = 0

    Steps to Solve:
    1. Factor the quadratic
    2. Apply the Zero – Product Property:
       Set each factor = 0 and solve for the variable
EXAMPLE: SOLVE EACH EQUATION BY
FACTORING
EXAMPLE: SOLVE EACH EQUATION BY
FACTORING
EXAMPLE: SOLVE EACH EQUATION BY
FACTORING
EXAMPLE: SOLVE EACH EQUATION BY
FACTORING
HOMEWORK
   P229 #1 – 3, 9 – 17 all

More Related Content

What's hot (6)

Newton cotes method
Newton cotes methodNewton cotes method
Newton cotes method
 
New microsoft office word document (2)
New microsoft office word document (2)New microsoft office word document (2)
New microsoft office word document (2)
 
Functions & Procedures [7]
Functions & Procedures [7]Functions & Procedures [7]
Functions & Procedures [7]
 
Prefix Postfix
Prefix PostfixPrefix Postfix
Prefix Postfix
 
Python operators part2
Python operators part2Python operators part2
Python operators part2
 
Seminar 2 coding_principles
Seminar 2 coding_principlesSeminar 2 coding_principles
Seminar 2 coding_principles
 

Similar to 4.5 quadratic equations

A110-4 solving factored polys
A110-4 solving factored polysA110-4 solving factored polys
A110-4 solving factored polys
vhiggins1
 
Presentation F Sharp
Presentation F Sharp Presentation F Sharp
Presentation F Sharp
guestbfe8bf
 
3.6 applications in optimization
3.6 applications in optimization3.6 applications in optimization
3.6 applications in optimization
math265
 
DEFINITION OF A QUADRATIC EQUATION A quadratic equatio
DEFINITION OF A QUADRATIC EQUATION A quadratic equatioDEFINITION OF A QUADRATIC EQUATION A quadratic equatio
DEFINITION OF A QUADRATIC EQUATION A quadratic equatio
LinaCovington707
 
Index cards characteristics and theorems
Index cards characteristics and theoremsIndex cards characteristics and theorems
Index cards characteristics and theorems
tschmucker
 

Similar to 4.5 quadratic equations (20)

A110-4 solving factored polys
A110-4 solving factored polysA110-4 solving factored polys
A110-4 solving factored polys
 
Derivatives in graphing-dfs
Derivatives in graphing-dfsDerivatives in graphing-dfs
Derivatives in graphing-dfs
 
1.6
1.61.6
1.6
 
Limit & Derivative Problems by ANURAG TYAGI CLASSES (ATC)
Limit & Derivative Problems by ANURAG TYAGI CLASSES (ATC)Limit & Derivative Problems by ANURAG TYAGI CLASSES (ATC)
Limit & Derivative Problems by ANURAG TYAGI CLASSES (ATC)
 
Exponent 2
Exponent 2Exponent 2
Exponent 2
 
Rules of exponents 1
Rules of exponents 1Rules of exponents 1
Rules of exponents 1
 
Basics of Optimization Theory
Basics of Optimization Theory Basics of Optimization Theory
Basics of Optimization Theory
 
Presentation F Sharp
Presentation F Sharp Presentation F Sharp
Presentation F Sharp
 
3.6 applications in optimization
3.6 applications in optimization3.6 applications in optimization
3.6 applications in optimization
 
DEFINITION OF A QUADRATIC EQUATION A quadratic equatio
DEFINITION OF A QUADRATIC EQUATION A quadratic equatioDEFINITION OF A QUADRATIC EQUATION A quadratic equatio
DEFINITION OF A QUADRATIC EQUATION A quadratic equatio
 
Midterm II Review
Midterm II ReviewMidterm II Review
Midterm II Review
 
Maxima & Minima of Functions - Differential Calculus by Arun Umrao
Maxima & Minima of Functions - Differential Calculus by Arun UmraoMaxima & Minima of Functions - Differential Calculus by Arun Umrao
Maxima & Minima of Functions - Differential Calculus by Arun Umrao
 
Maxima & Minima
Maxima & MinimaMaxima & Minima
Maxima & Minima
 
Polynomial Functions Review
Polynomial Functions ReviewPolynomial Functions Review
Polynomial Functions Review
 
Index cards characteristics and theorems
Index cards characteristics and theoremsIndex cards characteristics and theorems
Index cards characteristics and theorems
 
E2
E2E2
E2
 
Group No 05, calculus.pptx
Group No 05, calculus.pptxGroup No 05, calculus.pptx
Group No 05, calculus.pptx
 
Boyd 4.6, 4.7
Boyd 4.6, 4.7Boyd 4.6, 4.7
Boyd 4.6, 4.7
 
course slides of Support-Vector-Machine.pdf
course slides of Support-Vector-Machine.pdfcourse slides of Support-Vector-Machine.pdf
course slides of Support-Vector-Machine.pdf
 
Calc 3.4
Calc 3.4Calc 3.4
Calc 3.4
 

More from leblance

Parent night contact&survey
Parent night contact&surveyParent night contact&survey
Parent night contact&survey
leblance
 
7.3 daqy 2
7.3 daqy 27.3 daqy 2
7.3 daqy 2
leblance
 
10.3 part 1
10.3 part 110.3 part 1
10.3 part 1
leblance
 
10.1 part2
10.1 part210.1 part2
10.1 part2
leblance
 
10.1 part 1
10.1 part 110.1 part 1
10.1 part 1
leblance
 
Ch 9 practice exam
Ch 9 practice examCh 9 practice exam
Ch 9 practice exam
leblance
 
5.4 synthetic division
5.4 synthetic division5.4 synthetic division
5.4 synthetic division
leblance
 
5.4 long division
5.4 long division5.4 long division
5.4 long division
leblance
 
9.3 Part 1
9.3 Part 19.3 Part 1
9.3 Part 1
leblance
 
9.1 9.2 9.3 using the graph calc
9.1 9.2 9.3 using the graph calc9.1 9.2 9.3 using the graph calc
9.1 9.2 9.3 using the graph calc
leblance
 
5.1 part 2
5.1 part 25.1 part 2
5.1 part 2
leblance
 
9.2 lin reg coeff of det
9.2 lin reg coeff of det9.2 lin reg coeff of det
9.2 lin reg coeff of det
leblance
 

More from leblance (20)

Parent night contact&survey
Parent night contact&surveyParent night contact&survey
Parent night contact&survey
 
7.3 daqy 2
7.3 daqy 27.3 daqy 2
7.3 daqy 2
 
7.3
7.37.3
7.3
 
7.1
7.17.1
7.1
 
7.2
7.27.2
7.2
 
10.3 part 1
10.3 part 110.3 part 1
10.3 part 1
 
10.2
10.210.2
10.2
 
10.1 part2
10.1 part210.1 part2
10.1 part2
 
10.1 part 1
10.1 part 110.1 part 1
10.1 part 1
 
Ch 9 practice exam
Ch 9 practice examCh 9 practice exam
Ch 9 practice exam
 
5.4 synthetic division
5.4 synthetic division5.4 synthetic division
5.4 synthetic division
 
5.4 long division
5.4 long division5.4 long division
5.4 long division
 
5.3
5.35.3
5.3
 
9.3 Part 1
9.3 Part 19.3 Part 1
9.3 Part 1
 
9.1 9.2 9.3 using the graph calc
9.1 9.2 9.3 using the graph calc9.1 9.2 9.3 using the graph calc
9.1 9.2 9.3 using the graph calc
 
5.2
5.25.2
5.2
 
5.1 part 2
5.1 part 25.1 part 2
5.1 part 2
 
5.1[1]
5.1[1]5.1[1]
5.1[1]
 
9.1
9.19.1
9.1
 
9.2 lin reg coeff of det
9.2 lin reg coeff of det9.2 lin reg coeff of det
9.2 lin reg coeff of det
 

Recently uploaded

Essentials of Automations: Optimizing FME Workflows with Parameters
Essentials of Automations: Optimizing FME Workflows with ParametersEssentials of Automations: Optimizing FME Workflows with Parameters
Essentials of Automations: Optimizing FME Workflows with Parameters
Safe Software
 
Future Visions: Predictions to Guide and Time Tech Innovation, Peter Udo Diehl
Future Visions: Predictions to Guide and Time Tech Innovation, Peter Udo DiehlFuture Visions: Predictions to Guide and Time Tech Innovation, Peter Udo Diehl
Future Visions: Predictions to Guide and Time Tech Innovation, Peter Udo Diehl
Peter Udo Diehl
 
Search and Society: Reimagining Information Access for Radical Futures
Search and Society: Reimagining Information Access for Radical FuturesSearch and Society: Reimagining Information Access for Radical Futures
Search and Society: Reimagining Information Access for Radical Futures
Bhaskar Mitra
 

Recently uploaded (20)

10 Differences between Sales Cloud and CPQ, Blanka Doktorová
10 Differences between Sales Cloud and CPQ, Blanka Doktorová10 Differences between Sales Cloud and CPQ, Blanka Doktorová
10 Differences between Sales Cloud and CPQ, Blanka Doktorová
 
From Daily Decisions to Bottom Line: Connecting Product Work to Revenue by VP...
From Daily Decisions to Bottom Line: Connecting Product Work to Revenue by VP...From Daily Decisions to Bottom Line: Connecting Product Work to Revenue by VP...
From Daily Decisions to Bottom Line: Connecting Product Work to Revenue by VP...
 
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024
 
Unsubscribed: Combat Subscription Fatigue With a Membership Mentality by Head...
Unsubscribed: Combat Subscription Fatigue With a Membership Mentality by Head...Unsubscribed: Combat Subscription Fatigue With a Membership Mentality by Head...
Unsubscribed: Combat Subscription Fatigue With a Membership Mentality by Head...
 
IoT Analytics Company Presentation May 2024
IoT Analytics Company Presentation May 2024IoT Analytics Company Presentation May 2024
IoT Analytics Company Presentation May 2024
 
Speed Wins: From Kafka to APIs in Minutes
Speed Wins: From Kafka to APIs in MinutesSpeed Wins: From Kafka to APIs in Minutes
Speed Wins: From Kafka to APIs in Minutes
 
"Impact of front-end architecture on development cost", Viktor Turskyi
"Impact of front-end architecture on development cost", Viktor Turskyi"Impact of front-end architecture on development cost", Viktor Turskyi
"Impact of front-end architecture on development cost", Viktor Turskyi
 
Bits & Pixels using AI for Good.........
Bits & Pixels using AI for Good.........Bits & Pixels using AI for Good.........
Bits & Pixels using AI for Good.........
 
AI for Every Business: Unlocking Your Product's Universal Potential by VP of ...
AI for Every Business: Unlocking Your Product's Universal Potential by VP of ...AI for Every Business: Unlocking Your Product's Universal Potential by VP of ...
AI for Every Business: Unlocking Your Product's Universal Potential by VP of ...
 
Assuring Contact Center Experiences for Your Customers With ThousandEyes
Assuring Contact Center Experiences for Your Customers With ThousandEyesAssuring Contact Center Experiences for Your Customers With ThousandEyes
Assuring Contact Center Experiences for Your Customers With ThousandEyes
 
Essentials of Automations: Optimizing FME Workflows with Parameters
Essentials of Automations: Optimizing FME Workflows with ParametersEssentials of Automations: Optimizing FME Workflows with Parameters
Essentials of Automations: Optimizing FME Workflows with Parameters
 
Designing Great Products: The Power of Design and Leadership by Chief Designe...
Designing Great Products: The Power of Design and Leadership by Chief Designe...Designing Great Products: The Power of Design and Leadership by Chief Designe...
Designing Great Products: The Power of Design and Leadership by Chief Designe...
 
Future Visions: Predictions to Guide and Time Tech Innovation, Peter Udo Diehl
Future Visions: Predictions to Guide and Time Tech Innovation, Peter Udo DiehlFuture Visions: Predictions to Guide and Time Tech Innovation, Peter Udo Diehl
Future Visions: Predictions to Guide and Time Tech Innovation, Peter Udo Diehl
 
From Siloed Products to Connected Ecosystem: Building a Sustainable and Scala...
From Siloed Products to Connected Ecosystem: Building a Sustainable and Scala...From Siloed Products to Connected Ecosystem: Building a Sustainable and Scala...
From Siloed Products to Connected Ecosystem: Building a Sustainable and Scala...
 
Mission to Decommission: Importance of Decommissioning Products to Increase E...
Mission to Decommission: Importance of Decommissioning Products to Increase E...Mission to Decommission: Importance of Decommissioning Products to Increase E...
Mission to Decommission: Importance of Decommissioning Products to Increase E...
 
Unpacking Value Delivery - Agile Oxford Meetup - May 2024.pptx
Unpacking Value Delivery - Agile Oxford Meetup - May 2024.pptxUnpacking Value Delivery - Agile Oxford Meetup - May 2024.pptx
Unpacking Value Delivery - Agile Oxford Meetup - May 2024.pptx
 
Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...
Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...
Empowering NextGen Mobility via Large Action Model Infrastructure (LAMI): pav...
 
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...
 
In-Depth Performance Testing Guide for IT Professionals
In-Depth Performance Testing Guide for IT ProfessionalsIn-Depth Performance Testing Guide for IT Professionals
In-Depth Performance Testing Guide for IT Professionals
 
Search and Society: Reimagining Information Access for Radical Futures
Search and Society: Reimagining Information Access for Radical FuturesSearch and Society: Reimagining Information Access for Radical Futures
Search and Society: Reimagining Information Access for Radical Futures
 

4.5 quadratic equations