Algebra Playlist
Lesson 377 of 404 · Discriminant Equation – Quadratic Formula – Real & Imaginary Solutions – Algebra · Basic studies
Discriminant Equation – Quadratic Formula – Real & Imaginary Solutions – Algebra
This algebra video tutorial explains how to use the discriminant formula on a quadratic equation to determine the number and type of solutions such as real solutions or imaginary solutions. This video contains plenty of examples and practice problems.
Here is a list of topics:
1. Discriminant Formula
2. Determining the number of solutions
3. Positive Discriminant – 2 Real Solutions
4. If Discriminant Equals Zero – 1 Real Solution
5. Negative Discriminant Value – 2 Imaginary Solutions
6. Quadratic Formula and Discriminant
- (f o g)(x)
- (fog)(x)
- 1 real solution
- 2 imaginary solutions
- 2 real solutions
- 2 variables
- 2x2
- 2x2 matrices
- 3 points
- 3 variables
- 3x3
- 3x3 matrices
- 6th grade
- 7th grade
- 8th grade
- a+bi
- Absolute Value
- Absolute Value Equations
- absolute value functions
- absolute value functions and graphs
- absolute value inequalities
- ac method
- act
- act math
- act math concepts
- act math examples
- act math formulas
- act math help
- act math lessons
- act math overview
- act math practice
- act math practice problems
- act math prep
- act math questions
- act math review
- act math strategies
- act math study guide
- act math tips and strategies
- act math word problems
- act prep
- act review
- add
- Adding
- adding and subtracting
- adding and subtracting polynomials
- addition
- Age
- age problems algebra
- age problems tricks
- age problems tricks and shortcuts
- age word problems
- age word problems in algebra
- airplane
- algebra
- algebra 1
- algebra 1 basics
- algebra 1 common core regents review
- algebra 1 crash course
- algebra 1 eoc review
- algebra 1 final exam review
- algebra 1 lessons
- algebra 1 lessons for 9th grade
- algebra 1 overview
- algebra 1 regents
- algebra 1 regents review
- algebra 1 review
- algebra 1 study guide
- algebra 2
- algebra 2 - exponents
- algebra 2 crash course
- algebra 2 introduction
- algebra 2 lessons
- algebra 2 review
- algebra 2 solving quadratic equations
- algebra basics
- algebra completing the square
- algebra equations
- algebra factoring
- algebra factoring polynomials
- algebra graphing linear equations
- algebra introduction
- algebra introduction - the basics
- algebra lessons
- algebra linear equations
- algebra overview
- algebra practice problems
- algebra quadratic equations
- algebra quadratic formula
- algebra review
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- algebra shortcut trick
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- algebra solving for x
- algebra solving linear equations
- algebra tutorial
- algebra variables and expressions
- algebraic expressions
- algera 1
- all solution
- annually
- answers
- appreciation
- arithmetic
- arithmetic mean
- arithmetic sequence
- arithmetic sequence and series
- arithmetic sequence formula
- arithmetic series
- Asymptotes
- AVERAGE
- ax+by=c
- axis of symmetry
- bacteria
- basic arithmetic
- basic introduction
- basics
- binomial coefficients
- binomial expansion
- binomial expansion theorem
- binomial theorem
- binomial theorem expansion
- binomial theorem finding coefficients
- binomial theorem pascal's triangle
- Binomials
- boat
- box and whisker plots
- brackets
- Calculus
- car value
- central tendency
- central tendency - mean median mode range
- central tendency in statistics
- change of base
- change of base formula
- Channel
- chemistry
- closed circle
- coefficients
- College Algebra
- college algebra basics
- college algebra completing the square
- college algebra introduction
- college algebra quadratic formula
- college algebra review
- combinations
- combinations formula
- Combining Like Terms
- common difference
- common ratio
- Completing the Square
- completing the square to solve quadratic equations
- completing the square with coefficient
- completing the square with fractions
- complex fractions
- complex fractions with negative exponents
- complex fractions with variables
- complex fractions with variables and exponents
- complex imaginary numbers
- Complex Numbers
- complex numbers algebra 2
- complex numbers radicals
- complex numbers standard form
- complex roots
- composite functions
- composite functions domain
- composite functions inverse
- composite functions with fractions
- composite functions with square roots
- Composition of Functions
- composition of functions algebra 2
- composition of functions precalculus
- Compound Inequalities
- compound inequalities and or
- compound interest
- compound interest and e
- compound interest continuously
- compound interest explained
- compound interest formula
- compound interest investment
- compound interest problems
- compounded continuously formula
- compounded monthly
- condense
- condense logarithmic expressions
- condensing
- conic sections
- conjugates
- constant K
- continuity
- Conversion
- converting standard form to vertex form
- coordinate geometry
- Cosine
- counting principle
- cramer's rule
- cramer's rule 2 linear equations
- cramer's rule 2x2
- cramer's rule 3 variables
- cramer's rule 3x3
- cramer's rule 3x3 matrices
- cube
- cube root
- cube roots
- cubic
- cubic functions
- cumulative relative frequency
- current()
- daily
- dashed line
- Data
- data interpretation
- data set
- data sets
- data table
- date sets statistics
- decimal
- decimal number
- decimal point
- decimals
- definite integral
- degree
- denominator
- Depreciation
- desmos
- determinant of 2x2 matrices
- determinant of 3x3 matrices
- Determinants
- determine if function is even odd or neither
- determine whether f is even odd or neither
- difference
- difference of perfect squares
- different bases
- different denominators
- Digits
- dimensional analysis
- direct and inverse variation
- direct and inverse variation word problems
- direct inverse and joint variation
- direct variation
- discrimant
- Discriminant
- discriminant formula
- discriminant of a quadratic equation
- distance
- distance rate time
- distance rate time word problems
- distance word problems
- Distributive Property
- divide
- dividing
- dividing exponents
- dividing radicals
- division
- division properties of exponents
- domain
- domain and range
- domain and range of a function
- domain and range of a graph
- domain and range of a quadratic function
- domain and range of exponential functions
- domain and range of logarithmic functions
- domain and range of rational functions
- domain and range of trigonometric functions
- domain of a square root function
- dot plots
- downstream
- elimination
- Elimination Method
- end behavior
- equation
- Equation of a Line
- equations
- evaluate logarithms
- Even
- even data set
- even digits
- even functions
- even odd functions
- even odd or neither functions
- even odd or neither functions algebraically
- even odd or neither functions graphs
- even odd properties
- even or odd functions
- examples
- expand logarithmic expressions
- expanding
- explained
- Exponent Rules
- exponential
- Exponential Decay
- exponential equations
- exponential form
- Exponential Function
- exponential functions
- exponential growth
- exponential growth and decay
- exponential growth and decay functions
- exponential growth and decay precalculus
- exponential growth and decay word problems
- Exponents
- exponents in algebra
- exponents in math
- extraneous solutions
- f(g(x))
- factor
- factored form
- factoring
- factoring binomials
- factoring by completing the square
- factoring by grouping
- factoring cubic polynomials
- factoring differemce of squares
- factoring polynomials
- factoring polynomials by grouping
- factoring polynomials by substitution
- factoring polynomials gcf
- factoring polynomials using synthetic division
- factoring quadratic equations
- factoring trinomials
- factoring trinomials ax2+bx+c
- factoring trinomials by trial and error
- factoring trinomials with leading coefficient 1
- factoring trinomials with leading coefficient not 1
- final exam review
- finding coefficients
- finding quadratic equation
- finding quadratic equation from graph
- finding terms
- finding the domain of a square root function
- finding the nth term
- finding zeros
- finite sum
- foil
- foil method
- foil method algebra
- foil method binomials
- foil method multiplication
- foil method polynomials
- foil method trinomials
- foil method with exponents
- formula
- Fractional Exponents
- fractional exponents and radicals
- fractions
- fractions to decimals
- frequency distribution table
- frequency tables
- function
- functions
- fundamental counting principle
- future
- future value
- GCF
- geometric mean
- geometric sequences
- geometric sequences and series
- Geometric Series
- geometry
- GFX
- given two points
- graph
- graphical method
- graphing
- graphing equations
- graphing exponential functions
- graphing exponential functions domain
- graphing exponential functions precalculus
- graphing exponential functions transformations
- graphing exponential functions with e
- graphing functions
- graphing inequalities
- graphing inequalities on a number line.
- Graphing Linear Equations
- graphing linear equations in slope intercept form
- graphing linear equations in standard form
- graphing linear equations in two variables
- graphing linear equations using x and y intercepts
- Graphing Linear Inequalities
- graphing linear inequalities in two variables
- graphing logarithmic functions
- graphing logarithmic functions asymptotes
- graphing logarithmic functions with transformations
- graphing logs
- graphing parabolas
- graphing polar equations
- graphing polynomial functions
- graphing quadratic equations
- graphing quadratic functions
- graphing quadratic functions in standard form
- graphing quadratic functions in vertex form
- graphing quadratic functions using transformations
- graphing radical equations
- graphing radical functions
- graphing radicals
- graphing rational functions
- graphing rational functions with asymptotes
- graphing rational functions with asymptotes and holes
- graphing sine and cosine functions
- graphing solutions
- graphing systems of linear inequalities
- graphing systems of linear inequalities in two variables
- graphing transformations
- graphing trignometric functions
- graphs
- GRE
- gre math
- gre math lessons
- gre math practice questions
- gre math prep
- gre math preparation
- gre math review
- gre math tips
- gre math tips and strategies
- gre math tips and tricks
- gre math tricks
- gre prep
- gre preparation
- gre test
- gre test prep
- greatest common factor
- Ground
- higher degree
- Histograms
- holes
- home value
- horizontal and vertical asymptotes
- horizontal asymptote
- horizontal asymptotes
- horizontal asymptotes of rational functions
- Horizontal Shift
- horizontal vertical and slant asymptote
- how to add fractions
- how to add fractions with unlike denominators
- how to add or subtract fractions
- how to add or subtract radicals
- how to add three fractions with different denominators
- how to divide two fractions
- how to factor
- how to factor a trinomial
- how to factor by grouping
- how to find all real and imaginary solutions
- how to graph equations
- how to graph linear equations in slope intercept form
- how to graph linear equations in standard form
- how to graph linear equations with inequalities
- how to graph quadratic functions in standard form
- how to graph quadratic functions in vertex form
- how to graph rational functions
- how to learn math fast
- how to multiply two fractions
- how to rationalize the denominator
- how to simplify radicals
- how to solve equations
- how to solve linear inequalities
- how to solve quadratic equations
- how to solve quadratic equations by completing the square
- how to solve quadratic equations by factoring
- how to solve systems of equations
- how to solve systems of equations by substitution
- how to solve systems of nonlinear equations
- how to subtract fractions
- how to write equations for parallel and perpendicular lines
- how to write equations for parallel lines
- how to write equations for perpendicular lines
- imaginary
- imaginary numbers
- imaginary numbers division
- imaginary numbers explained
- imaginary numbers exponents
- imaginary solution
- imaginary solutions
- imaginary zeros
- improper fractions
- Inequalities
- inequalities algebra
- inequalities interval notation
- inequalities on a number line
- inequalities with absolute value
- inequalities with fractions
- infinite discontinuity
- Infinite sum
- infinitely many solutions
- infinity
- intercept
- intercept form
- intercepts
- intermediate algebra
- intermediate algebra factoring
- intermediate algebra lessons
- intermediate algebra review
- interquartile range
- Interval Notation
- intro to exponents
- Introduction
- introduction to exponents
- inverse
- Inverse Function
- inverse functions
- inverse functions algebra 2
- inverse functions calculus
- inverse functions domain and range
- inverse functions logarithms
- inverse functions precalculus
- inverse functions with fractions
- inverse variation
- joint variation
- km/hr
- leading coefficient
- leading term
- learn math fast
- lecture
- lessons
- limits
- line
- linear
- Linear Equation
- linear equations
- linear functions
- Linear Inequalities
- Lines
- ln
- logarithmic equations
- logarithmic expressions
- logarithmic functions
- logarithms
- logarithms explained
- logarithms review
- logarithms rules
- logs
- long division
- Long Division of Polynomials
- long division of polynomials made easy
- long division of polynomials with missing terms
- long division of polynomials with remainder
- made easy
- marbles
- Math
- math for adults
- math for kids
- math help
- math lessons
- math problems
- math tricks
- math tutorial videos
- math videos
- Matrices
- matrices and determinants
- matrices cramer's rule
- Matrix
- maxima
- maximum
- maximum height
- Mean
- mean median mode
- mean median mode and range
- median
- midterm review
- miles
- minima
- minimum
- missing
- missing terms
- mixed fractions
- mixed number to improper fraction
- mixed numbers
- MODE
- monomials binomials trinomials
- monthly
- mph
- multiplication
- multiplication properties of exponents
- multiplicity
- multiply
- multiplying
- multiplying and dividing
- multiplying and dividing polynomials
- multiplying binomials
- multiplying binomials and trinomials
- multiplying by the conjugate number
- multiplying exponents
- multiplying imaginary numbers
- multiplying powers with different bases
- multiplying powers with the same base
- multiplying radicals
- multiplying trinomials
- multiplying trinomials with binomials
- mutual funds
- natural logs
- negative
- Negative Exponents
- negative fractional exponents
- negative numbers
- No Solution
- nonlinear equations
- nth term
- number line
- Numbers
- oblique asymptote
- oblique asymptotes
- oblique asymptotes of rational functions
- odd
- odd data set
- odd functions
- one to one
- online
- online graphing calculator
- open circle
- Operations
- order of operations
- order of operations with absolute value
- order of operations with brackets
- order of operations with decimals
- order of operations with exponents
- order of operations with exponents and parentheses
- order of operations with fractions
- order of operations with integers
- order of operations with negative numbers
- order of operations with parentheses
- order of operations with square roots
- organic chemistry tutor
- outliers
- pair of points
- parabola
- parabolic functions
- parallel
- parallel and perpendicular lines
- parallel and perpendicular lines equations
- Parallel lines
- parent function
- parent functions
- parent functions algebra 2
- parent functions and their graphs
- parent functions and transformations
- parent functions domain and range
- parent functions precalculus
- parentheses
- Part
- part part whole
- partial sum
- pascal's triangle
- pascal's triangle binomial expansion
- pascal's triangle combinations
- pascal's triangle explained
- past
- past present future
- Patreon
- patreon channel
- patreon review
- patreon rewards
- patreon rewards tutorial
- patreon tutorial
- patreon tutorial video
- patreon video
- PEMDAS
- percent to decimal
- percentages
- percentile
- perfect cubes
- perfect squares
- permutations
- permutations and combinations
- permutations and combinations basics
- permutations and combinations tutorial
- permutations and combinations word problems
- perpendicular
- perpendicular lines
- piecewise
- Piecewise Functions
- piecewise functions absolute value
- piecewise functions continuity
- piecewise functions domain and range
- piecewise functions graphing
- piecewise functions limits
- plane
- Plotting Points
- point
- point discontinuity
- point slope form
- points of discontinuity
- polynomial equations
- polynomial expressions
- polynomial function
- polynomial functions
- polynomial functions end behavior
- polynomial functions finding zeros
- polynomial functions multiplicity
- polynomials
- population growth
- population mean
- population standard deviation
- positive
- practice
- practice problems
- prealgebra
- Precalculus
- present
- present value
- probability
- probability basics
- probability compound events
- probability examples
- probability explained
- probability independent events
- probability problems
- probability review
- probability rules
- probability using marbles
- probability with marbles
- probability with replacement
- probability without replacement
- probability word problems
- problems
- properties
- properties of exponents
- properties of logarithms
- proportions
- proportions and ratios
- proportions with fractions
- proportions word problems
- quadratic
- Quadratic equation
- quadratic equations
- quadratic equations completing the square
- quadratic equations with fractions
- quadratic expressions
- quadratic form
- Quadratic Formula
- quadratic formula discriminant
- quadratic formula explained
- quadratic function
- Quadratic Functions
- quantitative comparisons
- quantity
- quarterly
- quartiles
- quizzes
- radical equations
- radical expressions
- radical function
- radical functions
- radicals
- range
- Rate
- ratio
- rational
- rational equations
- rational exponents
- rational expressions
- rational functions
- rational zeros
- rationalize
- rationalize the denominator
- rationalize the denominator and simplify
- rationalize the denominator with cube roots
- rationalize the denominator with radicals
- rationalize the denominator with radicals and variables
- rationalize the denominator with square roots
- rationalize the denominator with variables
- Ratios
- ratios and proportions
- Real
- real and imaginary solutions
- real and imaginary zeros
- real solution
- real solutions
- real zeros
- recursive
- recursive formula
- Reflection
- reflection origin
- reflection x-axis
- reflection y-axis
- relative frequency
- remainder
- remainder theorem
- repeating decimals
- review
- rewards
- rise over run
- roots
- Rules of Exponents
- sample mean
- sample standard deviation
- sat
- sat algebra
- sat algebra and functions
- sat functions
- sat geometry
- sat geometry review
- sat hard math questions
- sat help
- SAT math
- sat math crash course
- sat math help
- sat math online course
- sat math overview
- sat math practice
- sat math prep
- sat math ratios
- sat math review
- sat math study guide
- sat math test
- sat math test problems
- sat math tips
- sat practice
- sat prep
- sat questions and answers
- sat test
- sat test prep
- Scientific Notation
- scientific notation adding and subtracting
- Scientific Notation Introduction
- scientific notation multiplication and division
- scientific notation to standard form
- semi annually
- sigma notation
- simplify
- simplifying
- simplifying algebraic expressions
- simplifying algebraic expressions combining like terms
- simplifying algebraic expressions with parentheses
- simplifying complex fractions
- simplifying complex fractions with exponents
- simplifying complex fractions with negative exponents
- simplifying complex fractions with variables and exponents
- simplifying exponents
- simplifying expressions
- simplifying expressions with negative exponents
- simplifying fractional exponents
- simplifying imaginary numbers
- simplifying logarithmic expressions
- simplifying logs
- simplifying polynomial expressions
- simplifying radical expressions
- simplifying radicals
- simultaneous equations
- simultaneous equations elimination method
- simultaneous equations graphical method
- simultaneous equations substitution method
- simultaneous equations with 3 variables
- simultaneous equations with fractions
- sine
- sine and cosine
- skewed left
- skewed right
- skewness
- slant asymptote
- slant asymptotes
- Slope
- slope and a point
- slope intercept method
- Slope-Intercept
- Slope-Intercept Form
- solid line
- solutions
- solve by graphing
- solve for r
- solve for t
- solving
- solving absolute value equations
- solving absolute value equations and inequalities
- solving absolute value equations no solution
- solving absolute value equations with fractions
- solving absolute value inequalities
- solving absolute value inequalities interval notation
- solving absolute value inequalities with fractions
- solving and graphing absolute value inequalities
- solving and graphing inequalities on a number line
- solving and graphing linear inequalities
- solving by elimination
- solving by substitution
- solving compound inequalities
- solving compound inequalities and graphing
- solving compound inequalities with fractions
- solving distance word problems
- Solving Equations
- solving equations with fractions
- solving equations with parentheses
- solving equations with variables on both sides
- solving exponential equations
- solving exponential equations in quadratic form
- solving exponential equations using logarithms
- solving exponential equations with e
- solving for x
- solving imaginary numbers
- solving inequalities
- solving inequalities interval notation
- solving inequalities using additon and subtraction
- solving inequalities with absolute value
- solving inequalities with fractions
- solving inequalities with variables on both sides
- solving linear equations
- solving linear equations with fractions
- solving linear inequalities
- solving logarithmic equations
- solving logarithmic equations with different bases
- solving multistep equations
- solving polynomial equations
- solving polynomial equations by factoring
- solving polynomial equations using synthetic division
- solving quadratic equations
- solving quadratic equations by completing the square
- solving quadratic equations by completing the square with fractions
- solving quadratic equations by factoring
- solving quadratic equations by factoring basic examples
- solving quadratic equations by factoring binomials
- solving quadratic equations by quadratic formula
- solving radical equations
- solving radical equations with cube roots
- solving radical equations with fractions
- solving radical equations with rational exponents
- solving radical equations with square roots
- solving radical equations with two radicals
- solving rational equations
- solving rational equations with different denominators
- solving rational equations with fractions
- solving rational equations with fractions and variables
- solving simultaneous equations
- solving systems of equations
- solving systems of equations by elimination
- solving systems of equations by elimination with 3 variables
- solving systems of equations by elimination with fractions
- solving systems of equations with 3 variables
- Solving Systems of Linear Equations
- solving systems of linear equations by elimination
- solving systems of linear equations in three variables
- solving systems of nonlinear equations
- solving systems of nonlinear equations in two variables
- speed
- speed distance time
- Square
- Square Root
- square root functions
- square root of decimal number
- square roots
- standard deviation
- standard deviation and variance
- standard deviation formula
- standard deviation statistics
- standard form
- standard form to vertex form
- standard form to vertex form completing the square
- standard form to vertex form with fractions
- statistics
- stem and leaf plots
- still water
- study guide
- substitution
- Substitution Method
- subtract
- subtracting
- subtraction
- sum
- sum and difference of perfect cubes
- sum and product
- summation notation
- symmetry
- synthetic division
- synthetic division and remainder theorem
- synthetic division factoring polynomials
- synthetic division to find zeros
- synthetic division with fractions
- synthetic division with polynomials
- System of Equations
- System of Linear Equations
- Systems of Equations
- systems of equations by graphing
- systems of equations inequalities
- systems of equations word problems
- Systems of Linear Equations
- systems of linear inequalities
- systems of nonlinear equations
- systems of nonlinear equations in two variables
- table
- table of values
- tail wind
- Tangent
- terms
- three variables
- time
- to find quotient and remainder
- to find roots
- to find zeros
- transformations
- Trigonometry
- Trinomials
- turning points
- tutorial
- tutorial video
- Two Variables
- Union
- unit conversion
- units
- unlike denominators
- upstream
- upstream downstream problems
- using logarithms
- using transformations
- variables
- variables on both sides
- variance
- vertex
- vertex form
- vertical asymptote
- vertical asymptotes
- vertical asymptotes and holes
- vertical asymptotes and horizontal asymptotes
- vertical asymptotes of rational functions
- Vertical Shift
- vertical stretch
- video
- weekly
- with asymptotes
- with e
- with i
- without a calculator
- Word Problems
- worksheet
- writing equations
- writing equations of lines
- writing equations of parallel and perpendicular lines
- writing linear equations
- writing quadratic equations
- writing quadratic equations in standard form
- writing quadratic equations in vertex form
- writing quadratic functions
- x and y intercepts
- x and y intercepts of a rational function
- x axis
- x intercepts
- x-intercept
- x=-b/2a
- Y Intercept
- y-y1=m(x-x1)
- y=a(x-h)^2+k
- y=ax^2+bx+c
- y=mx+b
- YouTube
- zero and negative exponents
- zero exponents
- zero of polynomial function
- Zeros