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Graphing a parabola by finding the roots and vertex | Quadratic equations | Algebra I | Khan Academy

Video vocabulary

intersect

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US / ˌɪntə'sekt /

UK / ˌɪntɚˈsɛkt /

B2
  • verb
  • To divide something by crossing it

plus

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US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

side

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US / saɪd /

UK / saɪd /

A1
  • 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

point

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US / pɔɪnt /

UK / pɔɪnt /

A1
  • noun
  • An item to be discussed
  • Small spot or dot
  • Fact or detail
  • Feature of something
  • The size of the text on a page or screen
  • A certain time or stage in a process
  • Certain position in time or space
  • Idea or fact you try to convince people about
  • Measurement of scores in a game, sport
  • Sharp end of something, e.g. a pen or pin
  • verb
  • To face a certain direction, e.g. north
  • To indicate something with your finger to others

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

route

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US / ru:t /

UK / rut, raʊt /

A2
  • noun
  • Way to get from one place to another place; path
  • Path or way that people often use
  • Method of achieving a certain result
  • verb
  • To send along a particular path or way

use

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US / ju:s /

UK / ju:s /

A1
  • 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

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US / raɪt /

UK / raɪt /

A1
  • 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

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US / ˈaɪðə(r) /

UK / ˈiðɚ, ˈaɪðɚ /

A1
  • 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

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

obviously

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US / ˈɒbviəsli /

UK / ˈɑːbviəsli /

A2
  • adverb
  • In a way that is obvious/easy to see or understand

quantity

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US / ˈkwɒntəti /

UK / ˈkwɑntɪti /

A2
  • noun
  • A large amount of something
  • Amount or number of something

axis

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US / ˈæksɪs /

UK / ˈæksɪs /

B1
  • noun
  • A line about which a rotating body turns

always

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US / 'ɔ:lweɪz /

UK / ˈɔlwez,-wɪz,-wiz /

A1
  • adverb
  • For a very long time
  • At all times; in every situation
  • For ever

already

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US / ɔ:lˈredi /

UK / ɔlˈrɛdi /

A1
  • adverb
  • Having happened or been done before this time

will

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US / wɪl /

UK / wɪl /

A1
  • 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

literally

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US / ˈlɪtərəli /

UK / ˈlɪtərəli /

B1
  • adverb
  • So as to express the exact meaning of something
  • Used to say something is true, even if unlikely

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

keep

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US / ki:p /

UK / kip /

A1
  • noun
  • Large, strong tower in the middle of a castle
  • Money spent on you so you can live in a place
  • verb
  • To continue doing something; not to stop
  • To stop balls going in a goal in sports
  • To not give back or return something
  • (Of food) to not spoil or not rot
  • To take possession of something to own, e.g. a pet
  • To have and continue to hold something
  • To do something that you have promised or agreed
  • To stay in a certain place or condition
  • To maintain the rules

symmetry

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US / ˈsɪmətri /

UK / ˈsɪmɪtri /

B2
  • noun
  • Having parts that are exactly the same

something

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US / ˈsʌmθɪŋ /

UK / ˈsʌmθɪŋ /

A1
  • adverb
  • In some degree or measure
  • noun
  • a person or thing of some value or consequence
  • pronoun
  • Thing that is not yet known or named
  • Approximately

another

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US / əˈnʌðə(r) /

UK / əˈnʌðɚ /

A1
  • adjecitve
  • One more, but not this
  • determiner
  • One more added
  • pronoun
  • One more (thing)

only

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US / ˈəunli /

UK / ˈonli /

A1
  • adverb
  • Just one; just that amount or thing; not more than
  • Not very important or serious
  • Just that type of thing, person
  • Short time ago; not before a certain time
  • conjunction
  • Except; but

put

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US / pʊt /

UK / pʊt /

A1
  • 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

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US / tu: /

UK / tu /

A1
  • number
  • 2

from

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US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

out

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US / aʊt /

UK / aʊt /

A1
  • 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

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • 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

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US / ˈmaɪnəs /

UK / ˈmaɪnəs /

A2
  • 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

where

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US / hwɛə /

UK / hwɛr, wɛr /

A1
  • conjunction
  • At or in the place which
  • In whatever place
  • pronoun
  • Word you use to ask the location of something

get

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US / ɡet /

UK / ɡɛt /

A1
  • 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

find

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US / faɪnd /

UK / faɪnd /

A1
  • noun
  • Object discovered by chance
  • Things that have been discovered from searching
  • verb
  • To become aware of something that is happening
  • To discover or meet by chance
  • To decide if someone is guilty of a crime, or not
  • To learn through study, research, or effort
  • To discover something by looking for it

mean

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US / mi:n /

UK / min /

A1
  • adjecitve
  • Being good at
  • Nasty; unkind
  • Not liking to spend money; cheap; stingy
  • noun
  • Average of a set of numbers
  • verb
  • To express a particular idea or thought
  • To intend to do something in particular
  • To have a particular meaning or value

right

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US / raɪt /

UK / raɪt /

A1
  • 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

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US / 'vælju: /

UK / ˈvælju /

A1
  • 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

down

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US / daʊn /

UK / daʊn /

A1
  • 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

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US / ðen /

UK / ðɛn /

A1
  • 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

happen

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US / 'hæpən /

UK / ˈhæpən /

A1
  • verb
  • To take place or occur

about

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US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

even

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US / 'i:vn /

UK / ˈivən /

A1
  • 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

like

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US / laɪk /

UK / laɪk /

A1
  • 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

people

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US / 'pi:pl /

UK / ˈpipəl /

A1
  • noun
  • Persons sharing culture, country, background, etc.
  • Men, Women, Children

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • 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

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • 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

number

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US / ˈnʌmbə(r) /

UK / ˈnʌmbɚ /

A1
  • noun
  • Symbols such as 1, 2, 56, 793
  • Particular song or dance performed during a show
  • Total quantity or amount of things
  • verb
  • To put numbers on things
  • To assign a sequence within a group, series, set
  • To claim to be part of a larger group, series, set

square

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US / skweə(r) /

UK / skwɛr /

A2
  • 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

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US / sɒlv /

UK / sɑ:lv /

A2
  • verb
  • To figure out a way to handle a difficult problem

all

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US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

figure

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US / ˈfiɡə /

UK / ˈfɪɡjɚ /

A1
  • 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

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US / weɪ /

UK / we /

A1
  • 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

bit

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US / bɪt /

UK / bɪt /

A1
  • 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

look

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US / lʊk /

UK / lʊk /

A1
  • 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

multiply

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US / ˈmʌltɪplaɪ /

UK / ˈmʌltəˌplaɪ /

B1
  • 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

rewrite

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US / ˌri:'raɪt /

UK / riˈraɪt /

A2
  • verb
  • To write again to improve, or correct errors

both

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US / bəuθ /

UK / boθ /

A1
  • determiner
  • Used to refer to two things at the same time
  • pronoun
  • Used to refer to two things at the same time

comma

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US / ˈkɒmə /

UK / ˈkɑ:mə /

B2
  • noun
  • Mark showing a pause or list in a sentence

work

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US / wɜ:k /

UK / wɚk /

A1
  • adjecitve
  • Activity completed in order to make money
  • noun
  • The product of some artistic or literary endeavor
  • Everything created by an author, artist, musician
  • Activity you do in order to make money
  • Place of employment
  • Final product or result of a some labor or effort
  • verb
  • To bring into a specific state of success
  • To be functioning properly, e.g. a car
  • To do your job in your company or workplace
  • To make an effort to do something
  • To operate a machine or device

add

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US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

take

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US / teɪk /

UK / tek /

A1
  • 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

between

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US / bɪˈtwi:n /

UK / bɪˈtwin /

A1
  • preposition
  • From one person, thing, or place, to another
  • In the space that separates two objects
  • Among two or more people who share something

swap

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US / swɒp /

UK / swɑp /

B2
  • noun
  • A trade or exchange of goods without using money
  • verb
  • To exchange goods without spending money; trade

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

expression

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US / ɪk'spreʃn /

UK / ɪkˈsprɛʃən /

A2
  • noun
  • Act of making your thoughts and feelings known
  • Group of words that have a specific meaning

paper

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US / ˈpeɪpə(r) /

UK / ˈpeɪpər /

A1
  • adjecitve
  • Not existing in reality, or done infrequently
  • Made from the material that we use to make books
  • noun
  • Academic writing or a talk on a specific topic
  • Written test
  • Newspaper
  • Pages of a book are made from this

subtract

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US / səbˈtrækt /

UK / səbˈtrækt /

B2
  • other
  • To take away a value or amount from another
  • verb
  • To take away a value or amount from another

several

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US / ˈsevrəl /

UK / ˈsɛvərəl,ˈsɛvrəl /

A1
  • adjecitve
  • Many of
  • pronoun
  • More than two but not a large amount

group

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US / ɡru:p /

UK / ɡrup /

A1
  • noun
  • Two or more musicians who play music together
  • Number of people or things gathered together
  • verb
  • To combine or collect objects or people together

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

complete

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US / kəm'pli:t /

UK / kəmˈplit /

A1
  • adjecitve
  • Being finished; done; achieved
  • Being as perfect and as total as could be
  • verb
  • To finish or reach the end of doing something

have

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US / həv /

UK / hæv /

A1
  • 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

last

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US / lɑ:st /

UK / læst /

A1
  • adjecitve
  • Most recent; the latest
  • The one before
  • adverb
  • Final; with nothing following; after all others
  • Most recent; the latest
  • determiner
  • The one at the end
  • verb
  • To remain or continue for a certain period of time

midpoint

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US / 'mɪdpɔɪnt /

UK / ˈmɪdˌpɔɪnt /

B1
  • noun
  • Point in or at the middle of something

part

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US / pɑ:t /

UK / pɑ:rt /

A1
  • 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

fall

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US / fɔ:l /

UK / fɔl /

A1
  • noun
  • Season after summer and before winter; Autumn
  • A drop in amount; decrease
  • Dropping from a standing position to the ground
  • verb
  • To drop in amount; to decrease
  • To come down from a higher position suddenly
  • To go from standing to the ground, by accident

problem

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US / ˈprɒbləm /

UK / ˈprɑbləm /

A1
  • adjecitve
  • Causing trouble
  • noun
  • Something difficult to deal with or causes trouble
  • Question to show understanding of a math concept

low

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US / ləʊ /

UK / lo /

A1
  • adjecitve
  • Having a small quantity, supply, or amount
  • Being unhappy or unpleasant in attitude
  • Not high; being near the ground, or bottom
  • (Of a voice, sound) being soft; quiet
  • noun
  • Situation of not having a lot of something

negative

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US / 'neɡətɪv /

UK / ˈnɛɡətɪv /

A2
  • 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

see

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US / si: /

UK / si /

A1
  • 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)

positive

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US / ˈpɒzətɪv /

UK / ˈpɑzɪtɪv /

A2
  • 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

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • 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)

talk

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US / tɔ:k /

UK / tɔk /

A1
  • noun
  • Style of speaking
  • Discussion between two countries
  • Giving information in front of people; lecture
  • Saying things or ideas to someone with words
  • verb
  • To make a formal speech about something
  • To say things or ideas to someone with words

ask

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US / ɑ:sk /

UK / æsk /

A1
  • verb
  • To say to someone that you want something

exact

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US / ɪɡ'zækt /

UK / ɪɡˈzækt /

A2
  • adjecitve
  • Completely correct; accurate; specific
  • verb
  • To get something, sometimes using force

express

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US / ɪk'spres /

UK / ɪkˈsprɛs /

A1
  • adjecitve
  • Sent by a fast mail service
  • Traveling at high speed
  • noun
  • Fast train or bus
  • verb
  • To send something by fast mail
  • To state or show what you think or how you feel

lower

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US / 'ləʊə(r) /

UK / ˈlaʊɚ, laʊr /

A2
  • adjecitve
  • In a position more near the bottom
  • verb
  • To move something downward to the ground

well

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US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

those

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US / ðəʊz /

UK / ðoz /

A1
  • determiner
  • The people or things we are talking about
  • pronoun
  • The objects far from the speaker

for

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US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

time

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US / taɪm /

UK / taɪm /

A1
  • 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

through

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US / θru: /

UK / θru /

A2
  • adjecitve
  • having finished using or doing something
  • adverb
  • From the beginning of something until the end
  • preposition
  • Over, in, across an entire thing or place
  • Allowing you to pass between, or to
  • By a particular way or process; by the use of

equation

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US / ɪˈkweɪʒn /

UK / ɪˈkweʒən, -ʃən /

B1
  • noun
  • Mathematical statement showing things to be equal
  • Complex set of different facts, ideas or issues

graph

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US / græf /

UK / ɡræf /

A2
  • noun
  • Image expressing numerical data in lines or shapes
  • verb
  • To show data using images

equal

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US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

intersection

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US / ˌɪntə'sekʃn /

UK / ˌɪntɚˈsɛkʃən /

B2
  • noun
  • Place where two things cross

now

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US / naʊ /

UK / naʊ /

A1
  • 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

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US / 'fɔ:mjələ /

UK / ˈfɔrmjələ /

A2
  • noun
  • A mathematical or scientific rule
  • Plan, rule or method for doing or making something

would

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US / wʊd /

UK / wʊd /

A1
  • 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

can

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US / kæn /

UK / kən,kæn /

A1
  • 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

parabola

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US / pəˈræbələ /

UK / pəˈræbələ /

A1
  • noun
  • Plane curve formed by intersecting other planes

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

give

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US / ɡɪv /

UK / ɡɪv /

A1
  • 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

same

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US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

vertex

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US / ˈvɜ:teks /

UK / ˈvɜ:rteks /

A1
  • noun
  • Summit; highest point; pl; vertices

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

lead

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US / li:d /

UK / lid /

A1
  • adjecitve
  • Being the main part in movies or plays
  • noun
  • Wire for electricity, computer, etc.; cable
  • Information that could help to solve a crime
  • Main part in a play or movie
  • Heavy, gray metal element
  • Rope used to tie something to stop it escaping
  • Act of being at the front in a race or game
  • verb
  • To show the way or guide others
  • To be at the front of a race or game
  • To travel in front of; go in advance of others

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

little

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US / 'lɪtl /

UK / ˈlɪtl /

A1
  • 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

the

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US / ðə /

UK / ðə /

A1
  • 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

also

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US / 'ɔ:lsəʊ /

UK / ˈɔlso /

A1
  • adverb
  • In addition; too; in a similar way

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

equally

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US / ˈi:kwəli /

UK / ˈiːkwəli /

A1
  • adverb
  • In an equal, even, or identical manner

multiple

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US / ˈmʌltɪpl /

UK / ˈmʌltəpəl /

B1
  • adjecitve
  • Having or involving more than one of something
  • noun
  • Number produced by multiplying a smaller number
  • Shop with many branches

into

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US / 'ɪntə /

UK / ˈɪntu /

A1
  • preposition
  • Moving or going inside something
  • In the same direction as; in the direction of
  • So as to become; taking the state of

other

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US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

perfect

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US / 'pɜ:fɪkt /

UK / ˈpɚfɪkt /

A1
  • adjecitve
  • So good it cannot be improved
  • verb
  • To do something so well, it cannot be done better

root

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US / ru:t /

UK / rut, rʊt /

A2
  • 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

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US / tɜ:n /

UK / tɚn /

A1
  • 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

this

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US / ðɪs /

UK / ðɪs /

A1
  • 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

valid

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US / 'vælɪd /

UK / ˈvælɪd /

A2
  • adjecitve
  • Being in effect or in force, often legally
  • Reasonable; based on sound assumptions
  • Working correctly; producing results

symmetrical

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US / sɪˈmetrɪkl /

UK / sɪˈmɛtrɪkəl /

B2
  • adjecitve
  • Having parts that are exactly the same

average

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US / 'ævərɪdʒ /

UK / ˈævərɪdʒ, ˈævrɪdʒ /

A2
  • adjecitve
  • Typical or normal; usual; ordinary
  • noun
  • Total of numbers divided by the number of items
  • verb
  • To add numbers then divide by the number of items

make

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US / meɪk /

UK / mek /

A1
  • 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

coefficient

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US / ˌkəʊɪˈfɪʃnt /

UK / ˌkoʊɪˈfɪʃnt /

B2
  • adjecitve
  • Number by which another number is multiplied

whose

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US / hu:z /

UK / huz /

A1
  • pronoun
  • Refers to the person who owns something
  • Subtitles section
  • We're asked to graph this function, finding the roots and the vertex of this parabola.
  • So to find the roots, when people talk about roots, they're talking about the points of intersection of this function and the x-axis.
  • So this is the x-axis here, and this is the y-axis.
  • And you're going to intersect the x-axis when y is equal to 0.
  • So to find the roots, we said y is equal to 0, so we solve the equation, x squared plus 4x minus 12 is equal to 0.
  • All I did is I said y is equal to 0, and I swapped the left- and right-hand sides.
  • Now, to factor this, we have a 1 as a leading coefficient, so we don't have to do the all out grouping.
  • We can just think, are there two numbers whose products are negative 12, and if I add them I get 4?
  • So let's think about it.
  • It looks like 2, positive 6, and negative 2 would work, if I go through all of negative 12's factors.
  • So this can be factored as x plus 6, times x minus 2.
  • 6 minus 2 is 4.
  • 6 times negative 2 is negative 12, so that's going to be equal to 0.
  • And if we have two numbers, and if, when you multiply them, they equal 0, that means that either x plus 6 is equal to 0, or x minus 2 is equal to 0.
  • Subtract 6 from both sides of this equation, you get x is equal to negative 6.
  • Add 2 to both sides of this equation, and you get x is equal to 2.
  • So y is equal to 0 when x is equal to negative 6, or x is equal to 2.
  • So let's graph both of those points.
  • x is equal to negative 6, y will be equal to 0.
  • So x is 1, 2, 3, 4, 5, 6.
  • So negative 6 comma 0.
  • That will be on the graph of this function, or the graph of this parabola.
  • And also the point, x is equal to 2.
  • So 1, 2.
  • Just like that. x is equal to 2.
  • So this is the point 2, 0.
  • Now to find the x value of the vertex, there's actually several ways of doing it.
  • There is a formula that gives it to you.
  • But actually, the easiest way to figure it out is it's actually going to be the midpoint between the two 0's.
  • If you already figured out the 0's, the x value where the vertex was going to lie-- because the two 0's are always symmetric around the axis of symmetry, which is the same x value as the vertex.
  • You can just find the midpoint of these two points, and that will be the x value of the vertex.
  • So let's just do that.
  • So if we take the midpoint, we can literally just average these two numbers.
  • So negative 6 plus 2, over 2 is negative 4 over 2, which is equal to negative 2.
  • So the vertex is x is equal to negative 2.
  • And when x is equal to negative 2, what is y?
  • So x is the vertex, and then y will be equal to negative 2 squared, is positive 4.
  • 4 times negative 2 is negative 8.
  • And then we have a minus 12 there.
  • So 4 minus 8 gets us to negative 4, minus another 12 is negative 16.
  • So the point negative 2, negative 16 is going to be our vertex.
  • So let me graph that.
  • I think it's going to fall off of this graph a little bit.
  • So negative 2, and then we're going to go 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 11, 12, 13, 14, 15, 16.
  • So it's going to be right around here.
  • We went off the graph paper.
  • But negative 2 all the way down to negative 16.
  • So that right there is the vertex.
  • Negative 2, negative 16.
  • All the way down here.
  • We can even lower the y-axis.
  • And so if I were going to graph the parabola, it would look something like this.
  • It would look something like that.
  • Just like that and obviously it would keep going.
  • Now, I figured out the vertex in this problem just by averaging the x values of the two routes.
  • That gave me the x value of the axis of symmetry, which is this right here. x is equal to negative 2.
  • That's the axis around which the parabola is symmetric.
  • The other way to figure out the x value of the vertex, is to use the formula, negative b over 2a.
  • So the x value of the vertex is equal to negative b-- negative 4-- over 2 times a.
  • a is 1, so over 2, which is also going to give you x is equal to negative 2.
  • Now, the last way to solve for the vertex is to complete the square on this parabola right here.
  • So what we can do is we can rewrite it.
  • We can say this is y is equal to x squared plus 4x.
  • I'm going to put the minus 12 out here.
  • And what we want to do is add and subtract the same number, so I can express this as a perfect square.
  • So if I take 1/2 of 4x, or if I take 1/2 of 4, I get 2 if I square that.
  • I could add a 4 here, and then subtract a 4.
  • And then what that does is it turns this into x plus 2 squared, right? x plus 2 squared is x squared plus 4x, plus 4.
  • We've seen that multiple times.
  • So you have x plus 2 squared.
  • And then you have the minus 4 minus 12, minus 16.
  • So this is just another way of writing this exact same function.
  • But when you write it this way you see that the lowest point, this part of the function right here is always positive.
  • It's a quantity squared.
  • The lowest value that it can be is 0.
  • But then it can only go up from 0.
  • So the lowest point, the lowest y value we can take on, is when this expression right here is 0.
  • And when that happens, the y value is negative 16.
  • Now, what x makes this value 0?
  • Well, x equals negative 2 will make this 0.
  • If you wanted to say, x plus 2 is equal to 0, this expression right here is going to be 0 when x plus 2 is equal to 0.
  • Subtract 2 from both sides, x is equal to negative 2.
  • So that's another way to find the vertex, all of them equally valid.