Example 5: Using the quadratic formula | Quadratic equations | Algebra I | Khan Academy
A1 A2 B1 B2 C1 C2
and
US / ənd /
•UK / ənd, ən,ænd /
- conjunction
- Used to refer to two or more things
- Plus; in addition; on top of that
- Used to introduce an action that follows another
magic
US / 'mædʒɪk /
•UK / ˈmædʒɪk /
- adjecitve
- Concerning or involving tricks for entertainment
- Being able to produce good results or success
- noun
- Attractive, appealing, and exciting quality
- Performance of tricks for entertainment
- Special ability or skill that causes success
- Use of the supernatural to make things happen
manipulate
US / mə'nɪpjʊleɪt /
•UK / məˈnɪpjəˌlet /
- verb
- To try to control others to gain an advantage
- To handle or work in a skillful manner
particular
US / pəˈtɪkjələ(r) /
•UK / pɚˈtɪkjəlɚ, pəˈtɪk- /
- adjecitve
- One specific (one)
- Having firm ideas about what is desirable
- Being special or more than is typical
version
US / ˈvə:ʃən /
•UK / ˈvɚʒən, -ʃən /
- noun
- Different way that someone interprets something
- New or different form of something
- An updated form of some software
over
US / 'əʊvə(r) /
•UK / ˈovɚ /
- adverb
- Finished; no longer happening
- Towards the ground/away from a standing position
- noun
- A set of six consecutive balls bowled in cricket
- other
- Finished
- preposition
- Showing the relation when a thing is above another
- On or covering something
- Above or across something
- More than you need
- From one side to the other
- In the direction of; toward
out
US / aʊt /
•UK / aʊt /
- adverb
- No longer stylish (e.g. fashion)
- Away from home, business, or the usual place
- In a direction/movement away from inside or center
- noun
- Act when a batter cannot continue playing
- verb
- To tell people a secret
minus
US / ˈmaɪnəs /
•UK / ˈmaɪnəs /
- adjecitve
- Being close to the bottom of a letter grade
- noun
- Negative quality; disadvantage
- Sign that indicates subtraction
- preposition
- Being less than zero in number
- Used when subtracting one number from another
- verb
- To take one number away from another; subtract
form
US / fɔ:m /
•UK / fɔrm /
- noun
- Sports team or person's current winning record
- Document you complete when making an application
- Visible shape or style; type; kind
- verb
- To organize something such as a club or group
- To develop; to come into a shape or substance
- To make something into a particular shape
from
US / frəm /
•UK / frʌm, frɑm,frəm /
- preposition
- Starting at a particular place, time or level
two
US / tu: /
•UK / tu /
- number
- 2
complete
US / kəm'pli:t /
•UK / kəmˈplit /
- adjecitve
- Being finished; done; achieved
- Being as perfect and as total as could be
- verb
- To finish or reach the end of doing something
could
US / kəd /
•UK / kʊd /
- other
- Past form of 'can' to mean have ability
- Used to ask for something politely, or to offer
have
US / həv /
•UK / hæv /
- verb
- To drink, smoke, eat or use something
- To experience the effects of something
- To organize an event, or join in an activity
- To own, possess, or hold something
- To cause to happen or produce a particular effect
radical
US / ˈrædɪkl /
•UK / ˈrædɪkəl,'rædɪkḷ /
- adjecitve
- Very new and different from what is traditional
- Concerning something's most basic part or form
- noun
- Person who believes in extreme political change
negative
US / 'neɡətɪv /
•UK / ˈnɛɡətɪv /
- adjecitve
- Being harmful, unwanted or unhelpful
- In mathematics, being less than zero
- Focusing on the bad aspects; pessimistic
- noun
- The opposite to a positive electrical charge
- In grammar, containing words such as 'no' or 'not'
- Reply to a question or statement that means 'no'
- Image on camera film used to make a photo
formula
US / 'fɔ:mjələ /
•UK / ˈfɔrmjələ /
- noun
- A mathematical or scientific rule
- Plan, rule or method for doing or making something
equal
US / 'i:kwəl /
•UK / ˈikwəl /
- adjecitve
- Same in shape, size, or number
- verb
- To add up or be the same as
can
US / kæn /
•UK / kən,kæn /
- noun
- A metal container for storing food
- other
- Able to; have the skill to; have the time to
- verb
- To have permission to
- To be possible to do
- To preserve food by sealing it in a metal container
would
US / wʊd /
•UK / wʊd /
- other
- Used to indicate something imagined
- Used to ask or request something politely
- Verb used to indicate possibility, request etc.
- Used to indicate a preference
- Used to indicate a reaction
- Indicates something that occurred repeatedly
- Used to indicate willingness or ability to do
really
US / ˈri:əli /
•UK / ˈriəˌli, ˈrili /
- adverb
- Used to stress something that is said; definitely
- In a true or accurate manner
- Very
principal
US / ˈprɪnsəpl /
•UK / ˈprɪnsəpəl /
- adjecitve
- Being the main or most important
- noun
- Leading person in a group of musicians or dancers
- Head teacher of a school
- Original amount of money borrowed
maybe
US / ˈmeɪbi /
•UK / ˈmebi /
- adverb
- Possibly but not certainly; perhaps
our
US / 'aʊə(r) /
•UK / aʊr /
- determiner
- Belonging to us
not
US / nɒt /
•UK / nɑt /
- adverb
- Word indicating the negative
- (Used to form the negative of verbs)
same
US / seɪm /
•UK / sem /
- adjecitve
- Being equal in quality and amount
- Identical; not different
- Not changing; constant
want
US / wɔnt /
•UK / wɑnt, wɔnt /
- noun
- Something you desire or wish for
- State or condition of poverty
- verb
- To desire or wish for something; hope for a thing
video
US / 'vɪdɪəʊ /
•UK / ˈvɪdiˌo /
- adjecitve
- Of a moving film, with sound
- noun
- Recording capturing action with sound
- verb
- To make a moving film of, with sound
give
US / ɡɪv /
•UK / ɡɪv /
- noun
- Degree of flexibility in something, a material
- verb
- To hand over or present something to someone
- To cause someone to have or experience something
good
US / ɡʊd /
•UK / ɡʊd /
- adjecitve
- Proper, appropriate or right
- (Of an amount) enough; plenty
- Excellent; high quality
- Acting well or properly; of moral character
- In a positive or happy emotional state
- noun
- Advantage or benefit
but
US / bət /
•UK / bʌt,bət /
- conjunction
- Used before you say something different, opposite
apply
US / ə'plaɪ /
•UK / əˈplaɪ /
- verb
- To spread a substance or liquid over a surface
- To commit your time and effort to doing something
- To make something useful in a certain situation
- To be relevant for a situation
- To ask formally for (job, permission etc.)
under
US / ˈʌndə(r) /
•UK / ˈʌndɚ /
- adjecitve
- In the same place as another thing, but lower
- adverb
- In a lower quantity or price than expected
- preposition
- According to the terms of an agreement or law
- Managed or controlled by the authority of
- Being of a lesser quality or amount than expected
- Influenced or affected by something or someone
- Less or lower in age, amount, size or number
standard
US / 'stændəd /
•UK / ˈstændəd /
- adjecitve
- Being the accepted normal level of quality
- (Of a language) being the most accepted in a place
- noun
- Official unit of measuring something
- Principle of behaving in a moral way
positive
US / ˈpɒzətɪv /
•UK / ˈpɑzɪtɪv /
- adjecitve
- Showing agreement or support for something
- Being sure about something; knowing the truth
- Having the charge produced by electrons
- Being good or useful
- Showing that a chemical is present in a test
fact
US / fækt /
•UK / fækt /
- noun
- Something that is known or proved to be true
just
US / dʒʌst /
•UK / dʒʌst /
- adjecitve
- Proper or appropriate; as is deserved
- Doing or being what is right or fair
- Legally correct; having enough evidence
- adverb
- Almost; nearly
- Exactly at the time of
- Exactly (the same as, like)
start
US / stɑ:t /
•UK / stɑrt /
- noun
- First time or place that a thing exists; beginning
- First opportunity to achieve something, e.g. a job
- Sudden action or movement because you are scared
- other
- Beginning of something in place or time
- verb
- To do, be or happen for the first time; begin
- To turn something on
exact
US / ɪɡ'zækt /
•UK / ɪɡˈzækt /
- adjecitve
- Completely correct; accurate; specific
- verb
- To get something, sometimes using force
ask
US / ɑ:sk /
•UK / æsk /
- verb
- To say to someone that you want something
time
US / taɪm /
•UK / taɪm /
- noun
- Speed at which music is played; tempo
- Point as shown on a clock, e.g. 3 p.m
- Number of hours, minutes needed to do something
- Occasion when something happens
- Period or occasion that something occurred
- Period in history or the past
- Something measured in minutes, hours, days, etc.
- How long an event takes; duration
- verb
- To check speed at which music is performed
- To choose a specific moment to do something
- To measure how long an event takes, e.g. a race
- To schedule something to occur at a specific moment
for
US / fə(r) /
•UK / fɔr,fə /
- preposition
- Used to show the purpose, or need of something
equation
US / ɪˈkweɪʒn /
•UK / ɪˈkweʒən, -ʃən /
- noun
- Mathematical statement showing things to be equal
- Complex set of different facts, ideas or issues
side
US / saɪd /
•UK / saɪd /
- adjecitve
- In addition to the central or most important thing
- Next to, or very close to, the right or left of
- noun
- Position or opinion that is opposite to another
- Right or left part of a person's body
- Feature of someone's personality
- Straight edge of an object
- One of two or more groups fighting each other
- verb
- To decide to agree with one point, not the other
rid
US / rɪd /
•UK / rɪd /
- verb
- To cause to no longer have (pest, problem)
plus
US / plʌs /
•UK / plʌs /
- noun
- A benefit or advantage
- preposition
- In addition; add
- In addition to; Indicates a number above
- Having a value greater than zero
write
US / raɪt /
•UK / raɪt /
- verb
- To compose letters and words on paper or a screen
- To invent or create a computer program
- To create a song or piece of music
use
US / ju:s /
•UK / ju:s /
- noun
- Ability to employ something
- Need to enable it to work
- Permission to do something with something
- Act of spending money
- Operation of a machine for its function
- verb
- To have; to eat, drink, consume etc.
- To need to operate or work
- To operate a machine, e.g. a computer
- To treat a person badly
- To do something with, for a task or purpose
actually
US / ˈæktʃuəli /
•UK / ˈæktʃuəli /
- adverb
- Used to add new (often different) information
here
US / hɪə(r) /
•UK / hɪr /
- adverb
- In this place; at this location, position or time
will
US / wɪl /
•UK / wɪl /
- noun
- Desire or choice of someone
- Document saying who gets your money when you die
- Strong desire to do something; determination
- Desire to do something; strong wish to do
- other
- Used with verbs to express the future
- verb
- To leave property to someone after your death
- To use mental effort to make something happen
- Am (is, are) likely to do
- To influence someone to do something
- To make something happen by strongly wanting it
ourselves
US / ɑ:ˈselvz /
•UK / aʊrˈsɛlvz, ɑr- /
- pronoun
- (Showing speaker is affected by their own action)
many
US / 'menɪ /
•UK / ˈmɛni /
- determiner
- Used to refer a large number of things
already
US / ɔ:lˈredi /
•UK / ɔlˈrɛdi /
- adverb
- Having happened or been done before this time
once
US / wʌns /
•UK / wʌns /
- adverb
- One time; one instance
- At a time in the past
- conjunction
- When; as soon as
divide
US / dɪ'vaɪd /
•UK / dɪˈvaɪd /
- verb
- To split numbers by another number, e.g. 6 / 2 = 3
- To separate something into equal pieces
quadratic
US / kwɒˈdrætɪk /
•UK / kwɑˈdrætɪk /
- adjecitve
- Polynomial of the second degree
place
US / pleɪs /
•UK / ples /
- noun
- Particular location, area or region
- verb
- To put someone in a particular type of situation
- To put something in a certain location or position
right
US / raɪt /
•UK / raɪt /
- adjecitve
- Correct or true
- The south side of you looking at the rising sun
- adverb
- Exactly in a place or time
- Being appropriate for a particular event
- In a straight or direct manner
- noun
- Something you are legally or morally allowed to do
- Ideal of what is just and good
- Political view based on conservatism
- verb
- To fix something previously wrong or unjust
- To make upright, as a boat that has turned over
first
US / fɜ:st /
•UK / fɚst /
- adjecitve
- 1st; Coming before all others in time or place
- noun
- Something that has not happened before
- Position of the winner of a competition
get
US / ɡet /
•UK / ɡɛt /
- verb
- To become affected by illness or disease
- To begin to feel or understand an emotion or idea
- To send or bring someone or something home, etc.
- To go somewhere to obtain something
- To (cause to) do a particular thing
- To obtain, receive or be given something
- To currently have
- To prepare for use
- To understand something being said or read
case
US / keɪs /
•UK / kes /
- noun
- Container used to carry things, e.g. clothes
- Set of facts about a crime
- Set of facts about an event
- Example or instance of something
- verb
- To find out about a place, as in planning to steal
then
US / ðen /
•UK / ðɛn /
- adverb
- A time that is not now
- Following another thing in time or arrangement
- Following on reasonably from what was just stated
- At that time, not now
derive
US / dɪˈraɪv /
•UK / dɪˈraɪv /
- verb
- To come from another thing
down
US / daʊn /
•UK / daʊn /
- adjecitve
- Being sad, sick, or unhappy
- Not operating, working, or functioning as expected
- adverb
- In a sitting or lying position
- Towards or on the ground, floor, or bottom
- Written or copied onto a piece of paper or book
- noun
- A period of play in American Football
- The soft, smooth hairs that cover a bird's body
- preposition
- Along something's path, course, or direction
- Going from a higher position to a lower position
- verb
- To eat or drink very quickly and without stopping
like
US / laɪk /
•UK / laɪk /
- adjecitve
- Being equal in status or kind to something else
- Similar; the same
- adverb
- For example
- preposition
- Used as a filler; used to ad emphasis
- In a way similar to the way something is done
- Such as; for example
- verb
- To want to
- To find something pleasing; to prefer something
what
US / wɒt /
•UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /
- pronoun
- Thing or things that; the same kind as
- Used to emphasize something you are about to say
- adjecitve
- Used to refer to a particular amount, or number
- Used to place emphasis on a particular quality
- adverb
- To a certain degree
- determiner
- Question words used for asking for information
- exclamation
- Used to express excitement, shock, or surprise
- Used to ask people to repeat something they said
that
US / ðæt /
•UK / ðæt, ðət /
- adjecitve
- The person or thing being talked about
- Used to identify something both the speakers know
- adverb
- Used to reinforce adjectives and adverbs
- To such a degree
- conjunction
- Used to connect a noun clause
- Used to introduce an adverbial clause
- Used to introduce a noun clause
- determiner
- Used as a noun to refer to something
- pronoun
- Referring an object far away
- Used to refer to the relative pronoun ‘which’
remind
US / rɪ'maɪnd /
•UK / rɪˈmaɪnd /
- verb
- To cause someone to remember what they forgot
people
US / 'pi:pl /
•UK / ˈpipəl /
- noun
- Persons sharing culture, country, background, etc.
- Men, Women, Children
even
US / 'i:vn /
•UK / ˈivən /
- adjecitve
- Being equal in influence, power, possibility etc.
- Being divided equally or fairly
- (Of teams/contest) with similar chances of success
- Smooth, level, or regular
- Can be divided by 2; ending in 2, 4, 6, 8, or 0
- At a regular, equally steady manner
- Remaining steady and unchanging
- adverb
- (When this is surprising) as well; too
- (Used to compare two things/stress the difference)
- verb
- To make something level; to flatten
- To make something equal
again
US / ə'ɡen /
•UK / əˈɡɛn /
- adverb
- One more time, once more
solve
US / sɒlv /
•UK / sɑ:lv /
- verb
- To figure out a way to handle a difficult problem
tell
US / tel /
•UK / tɛl /
- verb
- To (strongly) advise a person to do something
- To be able to guess
- To say or communicate information to someone
- To inform, but without speaking; indicate
- To have a negative effect on someone
- To order someone to do something; command
- To recognize something based on certain signs
- To report something to an authority
- To explain something or teach someone something
square
US / skweə(r) /
•UK / skwɛr /
- adjecitve
- Being fair or honest
- Multiply a number by itself e.g. 2x2 or 6x6
- noun
- Shape with 4 equal length sides and 4 equal angles
- The result of multiplying Length by the width
- Open public area in the middle of the town
- verb
- To make something balance or be equal
- To multiply a number by itself, e.g. 2x2 or 6x8
- To straighten the edge to form a four-sided shape
twice
US / twaɪs /
•UK / twaɪs /
- adverb
- Two times
way
US / weɪ /
•UK / we /
- adverb
- Used to emphasize the amount of something
- noun
- Particular aspect of something being thought about
- One of various choices that could be made
- Particular existing condition or state
- (Often long) distance or length of time
- How something is done
- Route to go to a place
- Small street
- Usual behavior, emotions or habits of someone
show
US / ʃəʊ /
•UK / ʃo /
- noun
- False display of love, emotion or action
- An event for displaying or promoting goods
- Play, opera or theater production
- Presentation that is broadcast on TV or radio
- verb
- To be easily seen or displayed
- To display your emotions or feelings
- To let someone see something; display
- To explain or teach how something is done
- To lead someone somewhere; point them to something
- To prove something to be true, correct
- To reveal or allow something to be seen
both
US / bəuθ /
•UK / boθ /
- determiner
- Used to refer to two things at the same time
- pronoun
- Used to refer to two things at the same time
all
US / ɔ:l /
•UK / ɔl /
- adverb
- Completely; totally
- determiner
- Being every one of something
- pronoun
- 100% of something; the complete amount
rewrite
US / ˌri:'raɪt /
•UK / riˈraɪt /
- verb
- To write again to improve, or correct errors
multiply
US / ˈmʌltɪplaɪ /
•UK / ˈmʌltəˌplaɪ /
- verb
- To increase in number by reproducing/having babies
- To increase something by a large quantity
- To have increased by a large quantity
- To calculate two numbers e.g. 2 x 4
general
US / 'dʒenrəl /
•UK / ˈdʒɛnərəl /
- adjecitve
- Widespread, normal or usual
- noun
- Top ranked officer in the army
they
US / ðeɪ /
•UK / ðe /
- pronoun
- Two or more people, animals, or things
take
US / teɪk /
•UK / tek /
- noun
- Filming of a single scene for TV or the movies
- verb
- To accept something that is offered
- To use a method of traveling, e.g. a bus or train
- To use a camera to make (a photo)
- To pick up something and go away with it
- To study a subject in school
- To attempt to pass (an exam)
- To require a certain amount of time, money, space
add
US / æd /
•UK / æd /
- verb
- To include as well
- To put two things or numbers together, e.g. 2+2
you
US / jʊ /
•UK / ju /
- pronoun
- Person someone is speaking or writing to
- Person or people in general
root
US / ru:t /
•UK / rut, rʊt /
- noun
- Emotional connection with a place, history etc.
- The origin or starting place of something
- A number that is multiplied by itself
- Part of plant growing underground, as to get water
- Part of tooth, hair etc. from which the rest grows
- Base part of a word to which affixes can be added
- verb
- To cause a plant to develop or grow roots
- (Animals) to search for e.g. food in earth
- To stop someone moving, as through fear
other
US / 'ʌðə(r) /
•UK / ˈʌðər /
- adjecitve
- A thing different from that mentioned
- determiner
- (Something) else; not the first (one)
- pronoun
- Being the one and only thing of that category
the
US / ðə /
•UK / ðə /
- article
- Used to refer to something already mentioned
- Used to show there is only one of something
- determiner
- Used to describe all of a family
let
US / let /
•UK / lɛt /
- verb
- To allow someone to do something
- Introducing a suggestion to do something together
- To rent a house, etc. to others
might
US / maɪt /
•UK / maɪt /
- other
- Used to politely request an action
- Used to express that something could happen
- Power, strength, force or influence
valid
US / 'vælɪd /
•UK / ˈvælɪd /
- adjecitve
- Being in effect or in force, often legally
- Reasonable; based on sound assumptions
- Working correctly; producing results
this
US / ðɪs /
•UK / ðɪs /
- adjecitve
- Used to indicate something already been discussed
- Used to indicate something happening around now
- adverb
- An indication by a physical motion or gesture
- A specific amount of
- determiner
- Person, thing, or idea near you
- pronoun
- Person, thing that has already been discussed
solution
US / səˈlu:ʃn /
•UK / səˈluʃən /
- noun
- Mix of a liquid and a solid or a gas
- Way to solve or deal with a problem
coefficient
US / ˌkəʊɪˈfɪʃnt /
•UK / ˌkoʊɪˈfɪʃnt /
- adjecitve
- Number by which another number is multiplied
answer
US / 'ɑ:nsə(r) /
•UK / ˈænsɚ /
- noun
- Reply to a question someone asks
- Solution to a problem or test question
- verb
- To reply to a question someone asks
- To solve a test question or a problem