Example 2: Using the quadratic formula | Quadratic equations | Algebra I | Khan Academy
A1 A2 B1 B2 C1 C2
figure
US / ˈfiɡə /
•UK / ˈfɪɡjɚ /
- noun
- Your body shape
- Numbers in a calculation
- Doll-like thing meant to represent a person
- Picture or diagram giving information in a text
- Person who is very important or famous
- Shape of a person seen indistinctly or in outline
- Amount that is expressed in numbers
- verb
- To appear in a game, play or event
- To calculate how much something will cost
- To understand after thinking; work out
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
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
all
US / ɔ:l /
•UK / ɔl /
- adverb
- Completely; totally
- determiner
- Being every one of something
- pronoun
- 100% of something; the complete amount
expression
US / ɪk'spreʃn /
•UK / ɪkˈsprɛʃən /
- noun
- Act of making your thoughts and feelings known
- Group of words that have a specific meaning
subtract
US / səbˈtrækt /
•UK / səbˈtrækt /
- other
- To take away a value or amount from another
- verb
- To take away a value or amount from another
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
original
US / ə'rɪdʒənl /
•UK / əˈrɪdʒənəl /
- adjecitve
- Being first made, thought or performed; fresh
- Being unique or thinking differently from others
bit
US / bɪt /
•UK / bɪt /
- noun
- Device put in a horse's mouth to control it
- Small piece of something
- verb
- (E.g. of fish) to take bait and be caught
cancel
US / 'kænsl /
•UK / ˈkænsəl /
- verb
- To end a legal, business, or other agreement
- To stop a planned event from happening
look
US / lʊk /
•UK / lʊk /
- noun
- Person's beauty or physical attractiveness
- Particular style of dress, clothes, or appearance
- The way someone, something appears to be
- Act of searching for or examining something
- verb
- To appear to be; seem
rewrite
US / ˌri:'raɪt /
•UK / riˈraɪt /
- verb
- To write again to improve, or correct errors
equal
US / 'i:kwəl /
•UK / ˈikwəl /
- adjecitve
- Same in shape, size, or number
- verb
- To add up or be the same as
now
US / naʊ /
•UK / naʊ /
- adverb
- At the present time or moment
- Right away or in the next possible moment
- Used to refer to something that just happened
- Time between the present and a moment in the past
- conjunction
- Resulting from or because of something
formula
US / 'fɔ:mjələ /
•UK / ˈfɔrmjələ /
- noun
- A mathematical or scientific rule
- Plan, rule or method for doing or making something
substitute
US / 'sʌbstɪtju:t /
•UK / ˈsʌbstɪˌtut, -ˌtjut /
- noun
- A person or thing acting in place of another
- verb
- To perform the tasks instead of someone else
- To replace one person or thing for another
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.)
but
US / bət /
•UK / bʌt,bət /
- conjunction
- Used before you say something different, opposite
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
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
become
US / bɪ'kʌm /
•UK / bɪˈkʌm /
- verb
- To begin to be; grow to be; develop into
- To be suitable for a particular job or role
same
US / seɪm /
•UK / sem /
- adjecitve
- Being equal in quality and amount
- Identical; not different
- Not changing; constant
really
US / ˈri:əli /
•UK / ˈriəˌli, ˈrili /
- adverb
- Used to stress something that is said; definitely
- In a true or accurate manner
- Very
color
US / 'kʌlə(r) /
•UK / ˈkʌlɚ /
- noun
- Quality of things you can see, e.g. red, blue
- Pink or red in your face, e.g. after being ill
- The shade of someone's skin e.g. black, or yellow
- verb
- To change or affect someone's opinion
- To make something colorful using colored pencils
not
US / nɒt /
•UK / nɑt /
- adverb
- Word indicating the negative
- (Used to form the negative of verbs)
our
US / 'aʊə(r) /
•UK / aʊr /
- determiner
- Belonging to us
constant
US / 'kɒnstənt /
•UK / ˈkɑnstənt /
- adjecitve
- Happening frequently or without pause
- noun
- Thing that happens always or at a regular rate
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
those
US / ðəʊz /
•UK / ðoz /
- determiner
- The people or things we are talking about
- pronoun
- The objects far from the speaker
green
US / gri:n /
•UK / ɡrin /
- adjecitve
- Color of young leaves
- Covered with vegetation, e.g. grass
- Concerned about protecting the environment
- The color of young leaves
- Lacking in experience/knowledge due to being young
- Being not fully grown or ripe, as in fruit
- noun
- Large grassy area
- used as a part of a name of a place (UK)
equation
US / ɪˈkweɪʒn /
•UK / ɪˈkweʒən, -ʃən /
- noun
- Mathematical statement showing things to be equal
- Complex set of different facts, ideas or issues
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)
for
US / fə(r) /
•UK / fɔr,fə /
- preposition
- Used to show the purpose, or need of 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
extend
US / ɪkˈstend /
•UK / ɪkˈstɛnd /
- verb
- To offer something (help, friendship) to someone
- To reach from one point to another
- To straighten or stretch something out, e.g. leg
- To make something last longer
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
put
US / pʊt /
•UK / pʊt /
- phrasal verb
- to make a light stop shining by pressing or moving a switch
- verb
- To move or place a thing in a particular position
- To rate something in importance or value
- To write or say something in a certain manner
two
US / tu: /
•UK / tu /
- number
- 2
far
US / fɑ:(r) /
•UK / fɑr /
- adjecitve
- A long way away
- Being a long way away
- adverb
- To a large degree or extent
leave
US / li:v /
•UK / liv /
- noun
- Permission to do something
- Vacation time; time off work
- verb
- To go away from; depart
- To gift property to someone after you die
- To allow something to continue happening
- To let something remain unused or available
- To let something or someone remain somewhere
from
US / frəm /
•UK / frʌm, frɑm,frəm /
- preposition
- Starting at a particular place, time or level
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
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
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
another
US / əˈnʌðə(r) /
•UK / əˈnʌðɚ /
- adjecitve
- One more, but not this
- determiner
- One more added
- pronoun
- One more (thing)
quadratic
US / kwɒˈdrætɪk /
•UK / kwɑˈdrætɪk /
- adjecitve
- Polynomial of the second degree
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
solve
US / sɒlv /
•UK / sɑ:lv /
- verb
- To figure out a way to handle a difficult problem
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
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
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
value
US / 'vælju: /
•UK / ˈvælju /
- noun
- Importance you attach to something
- Some information expressed as a number
- Stated price of something; worth
- verb
- To place a high importance on something
- To say how much money something is worth
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
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’
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
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
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
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
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
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
see
US / si: /
•UK / si /
- verb
- To go on a date with someone
- To predict whether something is, or will be true
- To understand what someone says
- To use your eyes to look at something
- To visit a place often for sightseeing or pleasure
- To visit or meet with someone
- To find out by waiting or looking
- To watch (a game, movie or TV show)
could
US / kəd /
•UK / kʊd /
- other
- Past form of 'can' to mean have ability
- Used to ask for something politely, or to offer
know
US / nəʊ /
•UK / noʊ /
- verb
- To be familiar with a person or place, thing
- To feel sure or be convinced about something
- To discover or be aware of something
- To be able to distinguish
- To have knowledge of things
hand
US / hænd /
•UK / hænd /
- noun
- Cards given to a player in a card game
- Piece of a clock that points to the time
- Someone who performs physical tasks or work
- Body part at the end of a person's arm
- Help for someone performing a particular action
- Condition of having power or influence
- Member of the crew of a ship
- verb
- To give something to someone personally
confuse
US / kənˈfju:z /
•UK / kənˈfjuz /
- verb
- To make something unclear or hard to understand
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
part
US / pɑ:t /
•UK / pɑ:rt /
- adjecitve
- To some degree; half; not fully
- noun
- Division of a book
- Ratio of something, e.g. 3 of gin, 1 of tonic
- A line in a person's hair, made with a comb
- Character an actor plays on stage, movie, or TV
- Some, but not all of a specific thing
- Role in causing something to happen
- verb
- To make a line in a person's hair, by using a comb
- To move two things apart creating a space
- To leave someone, or to break off a relationship
imagine
US / ɪ'mædʒɪn /
•UK / ɪˈmædʒɪn /
- verb
- To think creatively about; form mental picture of
divide
US / dɪ'vaɪd /
•UK / dɪˈvaɪd /
- verb
- To split numbers by another number, e.g. 6 / 2 = 3
- To separate something into equal pieces
satisfy
US / ˈsætɪsfaɪ /
•UK / ˈsætɪsˌfaɪ /
- verb
- To make someone happy because they got their wish
- To do what is required in order to finish
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
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
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
weird
US / wɪəd /
•UK / wɪrd /
- adjecitve
- Odd or unusual; surprising; strange
realize
US / 'ri:əlaɪz /
•UK / ˈriəˌlaɪz /
- verb
- To become aware of or understand mentally
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
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
either
US / ˈaɪðə(r) /
•UK / ˈiðɚ, ˈaɪðɚ /
- adjecitve
- One of two (used when there is a choice of two)
- adverb
- (After negative statements) likewise, in addition
- conjunction
- Used as the first of two connected things
- determiner
- Used as the first of two connected things
- pronoun
- The one or the other
here
US / hɪə(r) /
•UK / hɪr /
- adverb
- In this place; at this location, position or time
also
US / 'ɔ:lsəʊ /
•UK / ˈɔlso /
- adverb
- In addition; too; in a similar way
you
US / jʊ /
•UK / ju /
- pronoun
- Person someone is speaking or writing to
- Person or people in general
order
US / 'ɔ:də(r) /
•UK / ˈɔrdɚ /
- noun
- Religious or social group, as of nuns
- Instructions to others to do what you want
- State in which things are neat and organized
- What you ask to buy, e.g. food in restaurant
- Social or political control of an area
- verb
- To put things in a sequence, e.g. a, b, c
- To give instructions to others to do what you want
- To ask for something you want to buy, e.g. a meal
make
US / meɪk /
•UK / mek /
- noun
- Product made by a particular company; brand
- verb
- To arrange or prepare something e.g. dinner
- To get to (a place) on time
- To gain the status of (teacher, lawyer, etc.)
- To create something by putting things together
- To earn a certain amount of money at a job
- To cause or force a person to do something
- To cause something to happen or be formed
little
US / 'lɪtl /
•UK / ˈlɪtl /
- adjecitve
- Being short in length of time
- Not great in size, amount, or degree; small
- Being very young or younger than others
- adverb
- By an amount or degree that is not very much
- Not often; rarely
- noun
- A person's name
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
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
into
US / 'ɪntə /
•UK / ˈɪntu /
- preposition
- Moving or going inside something
- In the same direction as; in the direction of
- So as to become; taking the state of
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
one
US / wʌn /
•UK / wʌn /
- pronoun
- You; we; people in general; someone
- The thing or person previously referred to
- adjecitve
- Used to refer to people generally
- Being a strong example of (something mentioned)
- number
- Number 1
perfect
US / 'pɜ:fɪkt /
•UK / ˈpɚfɪkt /
- adjecitve
- So good it cannot be improved
- verb
- To do something so well, it cannot be done better
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
turn
US / tɜ:n /
•UK / tɚn /
- noun
- Place where changing of direction happens
- Your time or chance to perform a duty
- Your chance to play or do in say a game
- Unexpected change, as in the weather
- verb
- To become (a particular age)
- To become a different quality, color, etc.
- To change the direction of something, e.g. a car
- To move in an opposite direction or position
- To shape metal with a spinning tool
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
term
US / tɜ:m /
•UK / tɚm /
- noun
- Conditions applying to an agreement, contract
- Length of time something is expected to happen
- Fixed period of weeks for learning at school
- The (precise) name given to something
- verb
- To call; give a name to
implicit
US / ɪm'plɪsɪt /
•UK / ɪmˈplɪsɪt /
- adjecitve
- Unquestioning and without doubt
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