SlideShare a Scribd company logo
Solving Quadratic Equations
using the Quadratic Formula
General equation of a quadratic:

ax 2 bx c 0

Quadratic Formula:

x

b

b2
2a

4ac

Page 3

You must get equation
equal to zero before you
determine a,b, and c.

Notice where the
letters come from for
the formula

We use the quadratic formula when something can not be factored.
However, it also works for factorable quadratic equations as well.
#10:

x

2

8 x 13 0

a 1
b
8 x

b2
2a

b

c 13

8

x

8
21
x

12

Before you can find
a,b, and c, you must
get equation = to 0.

4 3

x

2 3

x

2

4ac

12
2

Simplify the radical

8 2 3
2
4

Type what is under
the radical exactly as
written on your
calculator.

4 1 13

8

Page 3

Divide by the denominator, if you can

3
Roots:
a 3
b 0
c

b2
2a

b

x
5

0
43
23
0

x
4 15
2 15

x

5

60
6

x

Solve the quadratic equation by using
the quadratic formula and leave
answers in simplest radical form.

4ac

2

0

x

60

Page 3

3x 2 5 0

#14:

2 15
6

15
3

Simplify the radical

Divide by the denominator, if you
can. Since I can’t, divide by GCF

Roots:
#16: x

2

a 1
b
12 x
c

b2
2a

b

29

12

x

12

28
2

x 8.64
x 8.6

12

Solve the quadratic equation by
using the quadratic formula and
round answers to the nearest tenth.

4ac

12
21

x
x

Page 3

12 x 29 0

2

4 1 29
Since we are solving to the nearest
tenth, we do not need to simplify
the radical!

28
2
x

12

28
2

x 3.35
x 3.4

Be careful when typing this into
your calculator. I recommend that
you type in the numerator then hit
enter, then divide by denominator!

Roots:
x 2 8 10 x
10x 10x

#25:

x

2

Solve the quadratic equation by
using the quadratic formula and
round answers to the nearest tenth.

10x 8 0

a 1
b
10

b

x

c 8

10

x

x

Page 3

10
2

b2
2a

4ac
2

10
21
10
68
x
2
68
10
x

x 9.12
x 9.1

41 8

68
2

x .87
x .9
Roots:
3x x 2

#25:

1

Page 3

3x 2 6 x 1
1
1

Solve the quadratic equation by
using the quadratic formula and
round answers to the nearest tenth.

3x 2 6 x 1 0
a
b
c

x

3
6

b2
2a

b

x

4ac

x

1

6

x

6
23
6

2

43

1

6

48

x

6

x 2.15
x 2.1

Roots

48
6

x
x

48
6

6

.15
.2
#25:

2x2
a
b

2x2 1 4x
4x
4x
4x 1 0

8

Solve the quadratic equation by using
the quadratic formula and leave
answers in simplest radical form.

2
4

x

b2
2a

b

c 1

x

Page 3

4

4 2

2 2

4
22
x
x

2

4ac

x

42 1
4

2

2
2
Roots:

8

4
4 2 2
4

Divide by the denominator, if you
can. Since I can’t, divide by GCF

More Related Content

What's hot

5.2 Solving Quadratic Equations by Factoring
5.2 Solving Quadratic Equations by Factoring5.2 Solving Quadratic Equations by Factoring
5.2 Solving Quadratic Equations by Factoringhisema01
 
Solving quadratic inequalities
Solving quadratic inequalitiesSolving quadratic inequalities
Solving quadratic inequalities
MartinGeraldine
 
Mathematics 9 Lesson 1-B: Solving Quadratic Equations using Quadratic Formula
Mathematics 9 Lesson 1-B: Solving Quadratic Equations using Quadratic FormulaMathematics 9 Lesson 1-B: Solving Quadratic Equations using Quadratic Formula
Mathematics 9 Lesson 1-B: Solving Quadratic Equations using Quadratic Formula
Juan Miguel Palero
 
Solving Quadratic Equations by Completing the Square
Solving Quadratic Equations by Completing the SquareSolving Quadratic Equations by Completing the Square
Solving Quadratic Equations by Completing the Square
Free Math Powerpoints
 
Factoring Perfect Square Trinomial
Factoring Perfect Square TrinomialFactoring Perfect Square Trinomial
Factoring Perfect Square Trinomial
Dhenz Lorenzo
 
Solving Quadratic Equations
Solving Quadratic EquationsSolving Quadratic Equations
Solving Quadratic Equations
Cipriano De Leon
 
7.2 Similar Polygons
7.2 Similar Polygons7.2 Similar Polygons
7.2 Similar Polygons
smiller5
 
4 5 fractional exponents
4 5 fractional exponents4 5 fractional exponents
4 5 fractional exponentsmath123b
 
Simplifying radical expressions, rational exponents, radical equations
Simplifying radical expressions, rational exponents, radical equationsSimplifying radical expressions, rational exponents, radical equations
Simplifying radical expressions, rational exponents, radical equationsJessica Garcia
 
Solving radical equations
Solving radical equationsSolving radical equations
Solving radical equations
Melchor Cachuela
 
Sum and product of the roots of a
Sum and product  of the roots of aSum and product  of the roots of a
Sum and product of the roots of a
MartinGeraldine
 
Adding and subtracting rational expressions
Adding and subtracting rational expressionsAdding and subtracting rational expressions
Adding and subtracting rational expressions
Dawn Adams2
 
QUADRATIC FUNCTIONS
QUADRATIC FUNCTIONSQUADRATIC FUNCTIONS
QUADRATIC FUNCTIONS
Maria Katrina Miranda
 
Nature of Roots of Quadratic Equation.pptx
Nature of Roots of Quadratic Equation.pptxNature of Roots of Quadratic Equation.pptx
Nature of Roots of Quadratic Equation.pptx
ssuser2b0f3a
 
Radicals
RadicalsRadicals
Radicals
Mark Ryder
 
Nature of the roots and sum and product of the roots of a quadratic equation
Nature of the roots and sum and product of the roots of a quadratic equationNature of the roots and sum and product of the roots of a quadratic equation
Nature of the roots and sum and product of the roots of a quadratic equation
Cipriano De Leon
 
Quadratic Equations in One Variables.pptx
Quadratic Equations in One Variables.pptxQuadratic Equations in One Variables.pptx
Quadratic Equations in One Variables.pptx
pandavlogsbyJM
 
Rectangular Coordinate System
Rectangular Coordinate SystemRectangular Coordinate System
Rectangular Coordinate System
Maria Romina Angustia
 
4 2 rules of radicals
4 2 rules of radicals4 2 rules of radicals
4 2 rules of radicalsmath123b
 

What's hot (20)

5.2 Solving Quadratic Equations by Factoring
5.2 Solving Quadratic Equations by Factoring5.2 Solving Quadratic Equations by Factoring
5.2 Solving Quadratic Equations by Factoring
 
Solving quadratic inequalities
Solving quadratic inequalitiesSolving quadratic inequalities
Solving quadratic inequalities
 
Mathematics 9 Lesson 1-B: Solving Quadratic Equations using Quadratic Formula
Mathematics 9 Lesson 1-B: Solving Quadratic Equations using Quadratic FormulaMathematics 9 Lesson 1-B: Solving Quadratic Equations using Quadratic Formula
Mathematics 9 Lesson 1-B: Solving Quadratic Equations using Quadratic Formula
 
Classifying Polynomials
Classifying PolynomialsClassifying Polynomials
Classifying Polynomials
 
Solving Quadratic Equations by Completing the Square
Solving Quadratic Equations by Completing the SquareSolving Quadratic Equations by Completing the Square
Solving Quadratic Equations by Completing the Square
 
Factoring Perfect Square Trinomial
Factoring Perfect Square TrinomialFactoring Perfect Square Trinomial
Factoring Perfect Square Trinomial
 
Solving Quadratic Equations
Solving Quadratic EquationsSolving Quadratic Equations
Solving Quadratic Equations
 
7.2 Similar Polygons
7.2 Similar Polygons7.2 Similar Polygons
7.2 Similar Polygons
 
4 5 fractional exponents
4 5 fractional exponents4 5 fractional exponents
4 5 fractional exponents
 
Simplifying radical expressions, rational exponents, radical equations
Simplifying radical expressions, rational exponents, radical equationsSimplifying radical expressions, rational exponents, radical equations
Simplifying radical expressions, rational exponents, radical equations
 
Solving radical equations
Solving radical equationsSolving radical equations
Solving radical equations
 
Sum and product of the roots of a
Sum and product  of the roots of aSum and product  of the roots of a
Sum and product of the roots of a
 
Adding and subtracting rational expressions
Adding and subtracting rational expressionsAdding and subtracting rational expressions
Adding and subtracting rational expressions
 
QUADRATIC FUNCTIONS
QUADRATIC FUNCTIONSQUADRATIC FUNCTIONS
QUADRATIC FUNCTIONS
 
Nature of Roots of Quadratic Equation.pptx
Nature of Roots of Quadratic Equation.pptxNature of Roots of Quadratic Equation.pptx
Nature of Roots of Quadratic Equation.pptx
 
Radicals
RadicalsRadicals
Radicals
 
Nature of the roots and sum and product of the roots of a quadratic equation
Nature of the roots and sum and product of the roots of a quadratic equationNature of the roots and sum and product of the roots of a quadratic equation
Nature of the roots and sum and product of the roots of a quadratic equation
 
Quadratic Equations in One Variables.pptx
Quadratic Equations in One Variables.pptxQuadratic Equations in One Variables.pptx
Quadratic Equations in One Variables.pptx
 
Rectangular Coordinate System
Rectangular Coordinate SystemRectangular Coordinate System
Rectangular Coordinate System
 
4 2 rules of radicals
4 2 rules of radicals4 2 rules of radicals
4 2 rules of radicals
 

Viewers also liked

Quadratic equations
Quadratic equationsQuadratic equations
Quadratic equations
debmegh
 
Quadratic formula
Quadratic formulaQuadratic formula
Quadratic formula
Anthony Quiatchon
 
The Discriminant
The DiscriminantThe Discriminant
The Discriminantdmidgette
 
College Algebra 1.4
College Algebra 1.4College Algebra 1.4
College Algebra 1.4Jeneva Clark
 
Use the Quadratic Formula
Use the Quadratic FormulaUse the Quadratic Formula
Use the Quadratic Formula
23Hagan
 
4.7 The Quadratic Formula
4.7 The Quadratic Formula4.7 The Quadratic Formula
4.7 The Quadratic Formulaleblance
 
Quadratic Equations
Quadratic EquationsQuadratic Equations
Quadratic Equations
Lily Maryati
 
11X1 T10 07 sum and product of roots (2010)
11X1 T10 07 sum and product of roots (2010)11X1 T10 07 sum and product of roots (2010)
11X1 T10 07 sum and product of roots (2010)Nigel Simmons
 
Algebra 2 unit 10.4
Algebra 2 unit 10.4Algebra 2 unit 10.4
Algebra 2 unit 10.4
Mark Ryder
 
50 solving equations by factoring
50 solving equations by factoring50 solving equations by factoring
50 solving equations by factoring
alg1testreview
 
8 4 Negative And Zero Exponents
8 4 Negative And Zero Exponents8 4 Negative And Zero Exponents
8 4 Negative And Zero Exponentstaco40
 
Algebra 2 unit 10.5
Algebra 2 unit 10.5Algebra 2 unit 10.5
Algebra 2 unit 10.5
Mark Ryder
 
Mathematics 9 Lesson 6: Rational Exponents
Mathematics 9 Lesson 6: Rational ExponentsMathematics 9 Lesson 6: Rational Exponents
Mathematics 9 Lesson 6: Rational Exponents
Juan Miguel Palero
 
Solving Equations by Factoring
Solving Equations by FactoringSolving Equations by Factoring
Solving Equations by Factoring
Josephine Neff
 
Simplifying expressions with negative and zero exponents
Simplifying expressions with negative and zero exponentsSimplifying expressions with negative and zero exponents
Simplifying expressions with negative and zero exponents
Genny Phillips
 
Quadratic Equation and discriminant
Quadratic Equation and discriminantQuadratic Equation and discriminant
Quadratic Equation and discriminantswartzje
 
AA Section 2-9
AA Section 2-9AA Section 2-9
AA Section 2-9
Jimbo Lamb
 
Solving quadratics with square roots
Solving quadratics with square rootsSolving quadratics with square roots
Solving quadratics with square rootsswartzje
 

Viewers also liked (20)

Quadratic equations
Quadratic equationsQuadratic equations
Quadratic equations
 
Quadratic formula
Quadratic formulaQuadratic formula
Quadratic formula
 
The Discriminant
The DiscriminantThe Discriminant
The Discriminant
 
College Algebra 1.4
College Algebra 1.4College Algebra 1.4
College Algebra 1.4
 
Use the Quadratic Formula
Use the Quadratic FormulaUse the Quadratic Formula
Use the Quadratic Formula
 
Bonus math project
Bonus math projectBonus math project
Bonus math project
 
4.7 The Quadratic Formula
4.7 The Quadratic Formula4.7 The Quadratic Formula
4.7 The Quadratic Formula
 
Quadratic Equations
Quadratic EquationsQuadratic Equations
Quadratic Equations
 
11X1 T10 07 sum and product of roots (2010)
11X1 T10 07 sum and product of roots (2010)11X1 T10 07 sum and product of roots (2010)
11X1 T10 07 sum and product of roots (2010)
 
Algebra 2 unit 10.4
Algebra 2 unit 10.4Algebra 2 unit 10.4
Algebra 2 unit 10.4
 
50 solving equations by factoring
50 solving equations by factoring50 solving equations by factoring
50 solving equations by factoring
 
8 4 Negative And Zero Exponents
8 4 Negative And Zero Exponents8 4 Negative And Zero Exponents
8 4 Negative And Zero Exponents
 
Math12 lesson2
Math12 lesson2Math12 lesson2
Math12 lesson2
 
Algebra 2 unit 10.5
Algebra 2 unit 10.5Algebra 2 unit 10.5
Algebra 2 unit 10.5
 
Mathematics 9 Lesson 6: Rational Exponents
Mathematics 9 Lesson 6: Rational ExponentsMathematics 9 Lesson 6: Rational Exponents
Mathematics 9 Lesson 6: Rational Exponents
 
Solving Equations by Factoring
Solving Equations by FactoringSolving Equations by Factoring
Solving Equations by Factoring
 
Simplifying expressions with negative and zero exponents
Simplifying expressions with negative and zero exponentsSimplifying expressions with negative and zero exponents
Simplifying expressions with negative and zero exponents
 
Quadratic Equation and discriminant
Quadratic Equation and discriminantQuadratic Equation and discriminant
Quadratic Equation and discriminant
 
AA Section 2-9
AA Section 2-9AA Section 2-9
AA Section 2-9
 
Solving quadratics with square roots
Solving quadratics with square rootsSolving quadratics with square roots
Solving quadratics with square roots
 

Similar to Quadratic Formula

Section 0.7 Quadratic Equations from Precalculus Prerequisite.docx
Section 0.7 Quadratic Equations from Precalculus Prerequisite.docxSection 0.7 Quadratic Equations from Precalculus Prerequisite.docx
Section 0.7 Quadratic Equations from Precalculus Prerequisite.docx
bagotjesusa
 
Mutiplyin and dividing expressions
Mutiplyin and dividing expressionsMutiplyin and dividing expressions
Mutiplyin and dividing expressionsfarahMM1
 
Matrices Questions & Answers
Matrices Questions & AnswersMatrices Questions & Answers
Matrices Questions & Answers
SantoshTamadaddi
 
Mutiplyin and dividing expressions
Mutiplyin and dividing expressionsMutiplyin and dividing expressions
Mutiplyin and dividing expressions
farahMM1
 
Quadratic equations
Quadratic equationsQuadratic equations
Quadratic equations
Numeric organisation
 
Quadratic Equations.ppt
Quadratic Equations.pptQuadratic Equations.ppt
Quadratic Equations.ppt
GURURAJUHS1
 
Determinants. Cramer’s Rule
Determinants. Cramer’s RuleDeterminants. Cramer’s Rule
Determinants. Cramer’s Rule
Елена Доброштан
 
WCS Specialist Maths An Introduction to Matrices PowerPoint
WCS Specialist Maths An Introduction to Matrices PowerPointWCS Specialist Maths An Introduction to Matrices PowerPoint
WCS Specialist Maths An Introduction to Matrices PowerPoint
Kingp18
 
1.basic of fractions
1.basic of fractions1.basic of fractions
1.basic of fractionsDreams4school
 
Vivek
VivekVivek
Day 5 - NOTES Completing the Square (1).ppt
Day 5  - NOTES Completing the Square (1).pptDay 5  - NOTES Completing the Square (1).ppt
Day 5 - NOTES Completing the Square (1).ppt
JosephForsuelo4
 
Gr-11-Maths-3-in-1-extract.pdf.study.com
Gr-11-Maths-3-in-1-extract.pdf.study.comGr-11-Maths-3-in-1-extract.pdf.study.com
Gr-11-Maths-3-in-1-extract.pdf.study.com
abenathixanga17
 
title-161104130731.pdfbbzbsjsbsbsbhshshsh
title-161104130731.pdfbbzbsjsbsbsbhshshshtitle-161104130731.pdfbbzbsjsbsbsbhshshsh
title-161104130731.pdfbbzbsjsbsbsbhshshsh
kdbdhawan
 
Completing the square v002
Completing the square v002Completing the square v002
Completing the square v002
cecilsie
 
Quadratic equations
Quadratic equationsQuadratic equations
Quadratic equations
Mervin Dayrit
 
Advance algebra
Advance algebraAdvance algebra
Advance algebra
lyra matalubos
 
1.4 Quadratic Equations
1.4 Quadratic Equations1.4 Quadratic Equations
1.4 Quadratic Equations
smiller5
 

Similar to Quadratic Formula (20)

Section 0.7 Quadratic Equations from Precalculus Prerequisite.docx
Section 0.7 Quadratic Equations from Precalculus Prerequisite.docxSection 0.7 Quadratic Equations from Precalculus Prerequisite.docx
Section 0.7 Quadratic Equations from Precalculus Prerequisite.docx
 
Mutiplyin and dividing expressions
Mutiplyin and dividing expressionsMutiplyin and dividing expressions
Mutiplyin and dividing expressions
 
Hprec2 2
Hprec2 2Hprec2 2
Hprec2 2
 
Matrices Questions & Answers
Matrices Questions & AnswersMatrices Questions & Answers
Matrices Questions & Answers
 
Quadratic Equations
Quadratic EquationsQuadratic Equations
Quadratic Equations
 
Mutiplyin and dividing expressions
Mutiplyin and dividing expressionsMutiplyin and dividing expressions
Mutiplyin and dividing expressions
 
Hprec2 5
Hprec2 5Hprec2 5
Hprec2 5
 
Quadratic equations
Quadratic equationsQuadratic equations
Quadratic equations
 
Quadratic Equations.ppt
Quadratic Equations.pptQuadratic Equations.ppt
Quadratic Equations.ppt
 
Determinants. Cramer’s Rule
Determinants. Cramer’s RuleDeterminants. Cramer’s Rule
Determinants. Cramer’s Rule
 
WCS Specialist Maths An Introduction to Matrices PowerPoint
WCS Specialist Maths An Introduction to Matrices PowerPointWCS Specialist Maths An Introduction to Matrices PowerPoint
WCS Specialist Maths An Introduction to Matrices PowerPoint
 
1.basic of fractions
1.basic of fractions1.basic of fractions
1.basic of fractions
 
Vivek
VivekVivek
Vivek
 
Day 5 - NOTES Completing the Square (1).ppt
Day 5  - NOTES Completing the Square (1).pptDay 5  - NOTES Completing the Square (1).ppt
Day 5 - NOTES Completing the Square (1).ppt
 
Gr-11-Maths-3-in-1-extract.pdf.study.com
Gr-11-Maths-3-in-1-extract.pdf.study.comGr-11-Maths-3-in-1-extract.pdf.study.com
Gr-11-Maths-3-in-1-extract.pdf.study.com
 
title-161104130731.pdfbbzbsjsbsbsbhshshsh
title-161104130731.pdfbbzbsjsbsbsbhshshshtitle-161104130731.pdfbbzbsjsbsbsbhshshsh
title-161104130731.pdfbbzbsjsbsbsbhshshsh
 
Completing the square v002
Completing the square v002Completing the square v002
Completing the square v002
 
Quadratic equations
Quadratic equationsQuadratic equations
Quadratic equations
 
Advance algebra
Advance algebraAdvance algebra
Advance algebra
 
1.4 Quadratic Equations
1.4 Quadratic Equations1.4 Quadratic Equations
1.4 Quadratic Equations
 

More from swartzje

Algebra 1 - EOC Practice Test
Algebra 1 - EOC Practice TestAlgebra 1 - EOC Practice Test
Algebra 1 - EOC Practice Test
swartzje
 
Swartz Factoring
Swartz FactoringSwartz Factoring
Swartz Factoring
swartzje
 
POLYNOMIAL NOTES Day #2
POLYNOMIAL NOTES Day #2POLYNOMIAL NOTES Day #2
POLYNOMIAL NOTES Day #2
swartzje
 
POLYNOMIALS - Add Subtract Multiply
POLYNOMIALS - Add Subtract MultiplyPOLYNOMIALS - Add Subtract Multiply
POLYNOMIALS - Add Subtract Multiply
swartzje
 
Polynomials Introduction
Polynomials IntroductionPolynomials Introduction
Polynomials Introduction
swartzje
 
Sig Figs and Accuracy
Sig Figs and AccuracySig Figs and Accuracy
Sig Figs and Accuracy
swartzje
 
Solving Systems - Elimination NOTES
Solving Systems - Elimination NOTESSolving Systems - Elimination NOTES
Solving Systems - Elimination NOTES
swartzje
 
Solving Systems by Substitution
Solving Systems by SubstitutionSolving Systems by Substitution
Solving Systems by Substitution
swartzje
 
Literal Equations Wed. 9/9 notes
Literal Equations Wed. 9/9 notesLiteral Equations Wed. 9/9 notes
Literal Equations Wed. 9/9 notes
swartzje
 
Solving Linear Equations with Notes
Solving Linear Equations with NotesSolving Linear Equations with Notes
Solving Linear Equations with Notes
swartzje
 
4 1 15 notes
4 1 15 notes4 1 15 notes
4 1 15 notes
swartzje
 
16.6 Quadratic Formula & Discriminant
16.6 Quadratic Formula & Discriminant16.6 Quadratic Formula & Discriminant
16.6 Quadratic Formula & Discriminant
swartzje
 
16.4 solving quadratics by completing the square
16.4 solving quadratics by completing the square16.4 solving quadratics by completing the square
16.4 solving quadratics by completing the square
swartzje
 
16.2 Solving by Factoring
16.2 Solving by Factoring16.2 Solving by Factoring
16.2 Solving by Factoring
swartzje
 
Factoring 15.3 and 15.4 Grouping and Trial and Error
Factoring 15.3 and 15.4 Grouping and Trial and ErrorFactoring 15.3 and 15.4 Grouping and Trial and Error
Factoring 15.3 and 15.4 Grouping and Trial and Error
swartzje
 
15.2 factoring x2+bx+c
15.2 factoring x2+bx+c15.2 factoring x2+bx+c
15.2 factoring x2+bx+c
swartzje
 
Factoring GCF and Grouping
Factoring GCF and GroupingFactoring GCF and Grouping
Factoring GCF and Grouping
swartzje
 
Multiplying special binomials
Multiplying special binomialsMultiplying special binomials
Multiplying special binomials
swartzje
 
Multiplying polynomials
Multiplying polynomialsMultiplying polynomials
Multiplying polynomials
swartzje
 
Multiplying Monomials
Multiplying MonomialsMultiplying Monomials
Multiplying Monomials
swartzje
 

More from swartzje (20)

Algebra 1 - EOC Practice Test
Algebra 1 - EOC Practice TestAlgebra 1 - EOC Practice Test
Algebra 1 - EOC Practice Test
 
Swartz Factoring
Swartz FactoringSwartz Factoring
Swartz Factoring
 
POLYNOMIAL NOTES Day #2
POLYNOMIAL NOTES Day #2POLYNOMIAL NOTES Day #2
POLYNOMIAL NOTES Day #2
 
POLYNOMIALS - Add Subtract Multiply
POLYNOMIALS - Add Subtract MultiplyPOLYNOMIALS - Add Subtract Multiply
POLYNOMIALS - Add Subtract Multiply
 
Polynomials Introduction
Polynomials IntroductionPolynomials Introduction
Polynomials Introduction
 
Sig Figs and Accuracy
Sig Figs and AccuracySig Figs and Accuracy
Sig Figs and Accuracy
 
Solving Systems - Elimination NOTES
Solving Systems - Elimination NOTESSolving Systems - Elimination NOTES
Solving Systems - Elimination NOTES
 
Solving Systems by Substitution
Solving Systems by SubstitutionSolving Systems by Substitution
Solving Systems by Substitution
 
Literal Equations Wed. 9/9 notes
Literal Equations Wed. 9/9 notesLiteral Equations Wed. 9/9 notes
Literal Equations Wed. 9/9 notes
 
Solving Linear Equations with Notes
Solving Linear Equations with NotesSolving Linear Equations with Notes
Solving Linear Equations with Notes
 
4 1 15 notes
4 1 15 notes4 1 15 notes
4 1 15 notes
 
16.6 Quadratic Formula & Discriminant
16.6 Quadratic Formula & Discriminant16.6 Quadratic Formula & Discriminant
16.6 Quadratic Formula & Discriminant
 
16.4 solving quadratics by completing the square
16.4 solving quadratics by completing the square16.4 solving quadratics by completing the square
16.4 solving quadratics by completing the square
 
16.2 Solving by Factoring
16.2 Solving by Factoring16.2 Solving by Factoring
16.2 Solving by Factoring
 
Factoring 15.3 and 15.4 Grouping and Trial and Error
Factoring 15.3 and 15.4 Grouping and Trial and ErrorFactoring 15.3 and 15.4 Grouping and Trial and Error
Factoring 15.3 and 15.4 Grouping and Trial and Error
 
15.2 factoring x2+bx+c
15.2 factoring x2+bx+c15.2 factoring x2+bx+c
15.2 factoring x2+bx+c
 
Factoring GCF and Grouping
Factoring GCF and GroupingFactoring GCF and Grouping
Factoring GCF and Grouping
 
Multiplying special binomials
Multiplying special binomialsMultiplying special binomials
Multiplying special binomials
 
Multiplying polynomials
Multiplying polynomialsMultiplying polynomials
Multiplying polynomials
 
Multiplying Monomials
Multiplying MonomialsMultiplying Monomials
Multiplying Monomials
 

Recently uploaded

2024.06.01 Introducing a competency framework for languag learning materials ...
2024.06.01 Introducing a competency framework for languag learning materials ...2024.06.01 Introducing a competency framework for languag learning materials ...
2024.06.01 Introducing a competency framework for languag learning materials ...
Sandy Millin
 
The Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official PublicationThe Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official Publication
Delapenabediema
 
Template Jadual Bertugas Kelas (Boleh Edit)
Template Jadual Bertugas Kelas (Boleh Edit)Template Jadual Bertugas Kelas (Boleh Edit)
Template Jadual Bertugas Kelas (Boleh Edit)
rosedainty
 
Operation Blue Star - Saka Neela Tara
Operation Blue Star   -  Saka Neela TaraOperation Blue Star   -  Saka Neela Tara
Operation Blue Star - Saka Neela Tara
Balvir Singh
 
Ethnobotany and Ethnopharmacology ......
Ethnobotany and Ethnopharmacology ......Ethnobotany and Ethnopharmacology ......
Ethnobotany and Ethnopharmacology ......
Ashokrao Mane college of Pharmacy Peth-Vadgaon
 
ESC Beyond Borders _From EU to You_ InfoPack general.pdf
ESC Beyond Borders _From EU to You_ InfoPack general.pdfESC Beyond Borders _From EU to You_ InfoPack general.pdf
ESC Beyond Borders _From EU to You_ InfoPack general.pdf
Fundacja Rozwoju Społeczeństwa Przedsiębiorczego
 
Introduction to Quality Improvement Essentials
Introduction to Quality Improvement EssentialsIntroduction to Quality Improvement Essentials
Introduction to Quality Improvement Essentials
Excellence Foundation for South Sudan
 
Model Attribute Check Company Auto Property
Model Attribute  Check Company Auto PropertyModel Attribute  Check Company Auto Property
Model Attribute Check Company Auto Property
Celine George
 
Digital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and ResearchDigital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and Research
Vikramjit Singh
 
The Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdfThe Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdf
kaushalkr1407
 
Instructions for Submissions thorugh G- Classroom.pptx
Instructions for Submissions thorugh G- Classroom.pptxInstructions for Submissions thorugh G- Classroom.pptx
Instructions for Submissions thorugh G- Classroom.pptx
Jheel Barad
 
How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17
Celine George
 
How libraries can support authors with open access requirements for UKRI fund...
How libraries can support authors with open access requirements for UKRI fund...How libraries can support authors with open access requirements for UKRI fund...
How libraries can support authors with open access requirements for UKRI fund...
Jisc
 
GIÁO ÁN DẠY THÊM (KẾ HOẠCH BÀI BUỔI 2) - TIẾNG ANH 8 GLOBAL SUCCESS (2 CỘT) N...
GIÁO ÁN DẠY THÊM (KẾ HOẠCH BÀI BUỔI 2) - TIẾNG ANH 8 GLOBAL SUCCESS (2 CỘT) N...GIÁO ÁN DẠY THÊM (KẾ HOẠCH BÀI BUỔI 2) - TIẾNG ANH 8 GLOBAL SUCCESS (2 CỘT) N...
GIÁO ÁN DẠY THÊM (KẾ HOẠCH BÀI BUỔI 2) - TIẾNG ANH 8 GLOBAL SUCCESS (2 CỘT) N...
Nguyen Thanh Tu Collection
 
Cambridge International AS A Level Biology Coursebook - EBook (MaryFosbery J...
Cambridge International AS  A Level Biology Coursebook - EBook (MaryFosbery J...Cambridge International AS  A Level Biology Coursebook - EBook (MaryFosbery J...
Cambridge International AS A Level Biology Coursebook - EBook (MaryFosbery J...
AzmatAli747758
 
How to Create Map Views in the Odoo 17 ERP
How to Create Map Views in the Odoo 17 ERPHow to Create Map Views in the Odoo 17 ERP
How to Create Map Views in the Odoo 17 ERP
Celine George
 
Palestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptxPalestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptx
RaedMohamed3
 
Thesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.pptThesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.ppt
EverAndrsGuerraGuerr
 
Chapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptxChapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptx
Mohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
 
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
siemaillard
 

Recently uploaded (20)

2024.06.01 Introducing a competency framework for languag learning materials ...
2024.06.01 Introducing a competency framework for languag learning materials ...2024.06.01 Introducing a competency framework for languag learning materials ...
2024.06.01 Introducing a competency framework for languag learning materials ...
 
The Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official PublicationThe Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official Publication
 
Template Jadual Bertugas Kelas (Boleh Edit)
Template Jadual Bertugas Kelas (Boleh Edit)Template Jadual Bertugas Kelas (Boleh Edit)
Template Jadual Bertugas Kelas (Boleh Edit)
 
Operation Blue Star - Saka Neela Tara
Operation Blue Star   -  Saka Neela TaraOperation Blue Star   -  Saka Neela Tara
Operation Blue Star - Saka Neela Tara
 
Ethnobotany and Ethnopharmacology ......
Ethnobotany and Ethnopharmacology ......Ethnobotany and Ethnopharmacology ......
Ethnobotany and Ethnopharmacology ......
 
ESC Beyond Borders _From EU to You_ InfoPack general.pdf
ESC Beyond Borders _From EU to You_ InfoPack general.pdfESC Beyond Borders _From EU to You_ InfoPack general.pdf
ESC Beyond Borders _From EU to You_ InfoPack general.pdf
 
Introduction to Quality Improvement Essentials
Introduction to Quality Improvement EssentialsIntroduction to Quality Improvement Essentials
Introduction to Quality Improvement Essentials
 
Model Attribute Check Company Auto Property
Model Attribute  Check Company Auto PropertyModel Attribute  Check Company Auto Property
Model Attribute Check Company Auto Property
 
Digital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and ResearchDigital Tools and AI for Teaching Learning and Research
Digital Tools and AI for Teaching Learning and Research
 
The Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdfThe Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdf
 
Instructions for Submissions thorugh G- Classroom.pptx
Instructions for Submissions thorugh G- Classroom.pptxInstructions for Submissions thorugh G- Classroom.pptx
Instructions for Submissions thorugh G- Classroom.pptx
 
How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17How to Make a Field invisible in Odoo 17
How to Make a Field invisible in Odoo 17
 
How libraries can support authors with open access requirements for UKRI fund...
How libraries can support authors with open access requirements for UKRI fund...How libraries can support authors with open access requirements for UKRI fund...
How libraries can support authors with open access requirements for UKRI fund...
 
GIÁO ÁN DẠY THÊM (KẾ HOẠCH BÀI BUỔI 2) - TIẾNG ANH 8 GLOBAL SUCCESS (2 CỘT) N...
GIÁO ÁN DẠY THÊM (KẾ HOẠCH BÀI BUỔI 2) - TIẾNG ANH 8 GLOBAL SUCCESS (2 CỘT) N...GIÁO ÁN DẠY THÊM (KẾ HOẠCH BÀI BUỔI 2) - TIẾNG ANH 8 GLOBAL SUCCESS (2 CỘT) N...
GIÁO ÁN DẠY THÊM (KẾ HOẠCH BÀI BUỔI 2) - TIẾNG ANH 8 GLOBAL SUCCESS (2 CỘT) N...
 
Cambridge International AS A Level Biology Coursebook - EBook (MaryFosbery J...
Cambridge International AS  A Level Biology Coursebook - EBook (MaryFosbery J...Cambridge International AS  A Level Biology Coursebook - EBook (MaryFosbery J...
Cambridge International AS A Level Biology Coursebook - EBook (MaryFosbery J...
 
How to Create Map Views in the Odoo 17 ERP
How to Create Map Views in the Odoo 17 ERPHow to Create Map Views in the Odoo 17 ERP
How to Create Map Views in the Odoo 17 ERP
 
Palestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptxPalestine last event orientationfvgnh .pptx
Palestine last event orientationfvgnh .pptx
 
Thesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.pptThesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.ppt
 
Chapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptxChapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptx
 
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
 

Quadratic Formula

  • 1. Solving Quadratic Equations using the Quadratic Formula General equation of a quadratic: ax 2 bx c 0 Quadratic Formula: x b b2 2a 4ac Page 3 You must get equation equal to zero before you determine a,b, and c. Notice where the letters come from for the formula We use the quadratic formula when something can not be factored. However, it also works for factorable quadratic equations as well.
  • 2. #10: x 2 8 x 13 0 a 1 b 8 x b2 2a b c 13 8 x 8 21 x 12 Before you can find a,b, and c, you must get equation = to 0. 4 3 x 2 3 x 2 4ac 12 2 Simplify the radical 8 2 3 2 4 Type what is under the radical exactly as written on your calculator. 4 1 13 8 Page 3 Divide by the denominator, if you can 3 Roots:
  • 3. a 3 b 0 c b2 2a b x 5 0 43 23 0 x 4 15 2 15 x 5 60 6 x Solve the quadratic equation by using the quadratic formula and leave answers in simplest radical form. 4ac 2 0 x 60 Page 3 3x 2 5 0 #14: 2 15 6 15 3 Simplify the radical Divide by the denominator, if you can. Since I can’t, divide by GCF Roots:
  • 4. #16: x 2 a 1 b 12 x c b2 2a b 29 12 x 12 28 2 x 8.64 x 8.6 12 Solve the quadratic equation by using the quadratic formula and round answers to the nearest tenth. 4ac 12 21 x x Page 3 12 x 29 0 2 4 1 29 Since we are solving to the nearest tenth, we do not need to simplify the radical! 28 2 x 12 28 2 x 3.35 x 3.4 Be careful when typing this into your calculator. I recommend that you type in the numerator then hit enter, then divide by denominator! Roots:
  • 5. x 2 8 10 x 10x 10x #25: x 2 Solve the quadratic equation by using the quadratic formula and round answers to the nearest tenth. 10x 8 0 a 1 b 10 b x c 8 10 x x Page 3 10 2 b2 2a 4ac 2 10 21 10 68 x 2 68 10 x x 9.12 x 9.1 41 8 68 2 x .87 x .9 Roots:
  • 6. 3x x 2 #25: 1 Page 3 3x 2 6 x 1 1 1 Solve the quadratic equation by using the quadratic formula and round answers to the nearest tenth. 3x 2 6 x 1 0 a b c x 3 6 b2 2a b x 4ac x 1 6 x 6 23 6 2 43 1 6 48 x 6 x 2.15 x 2.1 Roots 48 6 x x 48 6 6 .15 .2
  • 7. #25: 2x2 a b 2x2 1 4x 4x 4x 4x 1 0 8 Solve the quadratic equation by using the quadratic formula and leave answers in simplest radical form. 2 4 x b2 2a b c 1 x Page 3 4 4 2 2 2 4 22 x x 2 4ac x 42 1 4 2 2 2 Roots: 8 4 4 2 2 4 Divide by the denominator, if you can. Since I can’t, divide by GCF