Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Online

    16
    ReputationRep:
    Describe a single transformation that would map the graph of y = x^2 + 2 onto the graph of y = 2x^2+ 4

    I put stretch by scale factor 2 in y direction and 1/2 in x direction, but answers just say stretch by sf 2 in y direction.

    I'm really confused by this... can someone explain it please? Thanks :/

    (graphs and functions are really annoying me and I'm forcing myself to understand them)
    Online

    20
    ReputationRep:
    so if f(x) is x2 + 2 then 2f(x) is 2( x2 + 2 )
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by amaraub)
    Describe a single transformation that would map the graph of y = x^2 + 2 onto the graph of y = 2x^2+ 4

    I put stretch by scale factor 2 in y direction and 1/2 in x direction, but answers just say stretch by sf 2 in y direction.

    I'm really confused by this... can someone explain it please? Thanks :/

    (graphs and functions are really annoying me and I'm forcing myself to understand them)
    Well if I stretch by s.f. 2 in the y direction and s.f. 1/2 in the x-dir I'd get \frac{y}{2}=(2x)^2+2
    • Thread Starter
    Online

    16
    ReputationRep:
    So for Describe a single transformation that would map the graph of y = x^2 + 2 onto the graph of y = x^2+4x+6

    I put translated by vector [-4,6] but the answer says translation by 2 units in -ve x direction. Is it because it's x^2, so you put -2 in instead of -4? Mad confused lol
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by amaraub)
    So for Describe a single transformation that would map the graph of y = x^2 + 2 onto the graph of y = x^2+4x+6

    I put translated by vector [-4,6] but the answer says translation by 2 units in -ve x direction. Is it because it's x^2, so you put -2 in instead of -4? Mad confused lol
    x^2+4x+6=(x+2)^2+2 which is a translation by -2 along the x-axis from x^2+2
    • Thread Starter
    Online

    16
    ReputationRep:
    (Original post by the bear)
    so if f(x) is x2 + 2 then 2f(x) is 2( x2 + 2 )
    So when you stretch in the y direction you times everything by the sf?
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by amaraub)
    So when you stretch in the y direction you times everything by the sf?
    The simple rule is that when you stretch in the y-dir by s.f. a, you simply take y and replace it by \frac{y}{a}. Similarly if its along the x-axis. Just take x and replace it by \frac{x}{a}.

    If it's a translation along the y-axis by b, then you take y and replace it by y-b. Similarly for the x-axis.

    Then all you need to do is just rearrange to get y=... or whatever form they ask for.


    EXAMPLE:

    y=x^2-4x+10 can be rewritten as y=(x-2)^2+6 which in turn gives y-4=(x-2)^2+2 which is clearly a translation by vector [2,4] from the graph y=x^2+2 as you simply replace x \mapsto (x-2) and y \mapsto (y-4)
    • Thread Starter
    Online

    16
    ReputationRep:
    [QUOTE=RDKGames;74371654]The simple rule is that when you stretch in the y-dir by s.f. a, you simply take y and replace it by \frac{y}{a}. Similarly if its along the x-axis. Just take x and replace it by \frac{x}{a}.

    Ok, so if I was to enlarge y=x^2 + 2 by sf 2 in Y direction I would do y/2=x^2+2 which makes y= 2x^2 + 4?

    And If I was to do enlarge by sf 2 in x direction I'd do y = (x/2)^2 + 2, which makes y = x^2 /4 +2?

    (Original post by RDKGames)
    EXAMPLE:

    y=x^2-4x+10 can be rewritten as y=(x-2)^2+6 which in turn gives y-4=(x-2)^2+2 which is clearly a translation by vector [2,4] from the graph y=x^2+2 as you simply replace x \mapsto (x-2) and y \mapsto (y-4)
    Ah ok. So since its x^2 + 2 -> x^2+4x+6 I would do

    y = (x+2)^2 +2, so its a translation by [-2,0]?

    Is that the main way to do it? Because for a harder question I would be a lot more difficult to see what to put into the bracket
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by amaraub)

    Ok, so if I was to enlarge y=x^2 + 2 by sf 2 in Y direction I would do y/2=x^2+2 which makes y= 2x^2 + 4?

    And If I was to do enlarge by sf 2 in x direction I'd do y = (x/2)^2 + 2, which makes y = x^2 /4 +2?



    Ah ok. So since its x^2 + 2 -> x^2+4x+6 I would do

    y = (x+2)^2 +2, so its a translation by [-2,0]?

    Is that the main way to do it? Because for a harder question I would be a lot more difficult to see what to put into the bracket
    That's the main way to do it, and you can clearly see these match the answers in your book - they're all correct. If you find one you cannot do using these principles, post it here and we'll give you a hint.
    • Thread Starter
    Online

    16
    ReputationRep:
    (Original post by RDKGames)
    That's the main way to do it, and you can clearly see these match the answers in your book - they're all correct. If you find one you cannot do using these principles, post it here and we'll give you a hint.
    Ok thanks man A level maths is legit killing me
    • Thread Starter
    Online

    16
    ReputationRep:
    (Original post by RDKGames)
    That's the main way to do it, and you can clearly see these match the answers in your book - they're all correct. If you find one you cannot do using these principles, post it here and we'll give you a hint.
    If i was to enlarge (x+9)^3 + 2(x+9)^2 + 10 by a scale factor of 2 in the y direction would I do y/2 = (x+9)^3 + 2(x+9)^2 + 10, which gives me

    2(x+9)^3 + 4(x+9)^2 + 20? I put it in desmos but it doesn't look right
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by amaraub)
    If i was to enlarge (x+9)^3 + 2(x+9)^2 + 10 by a scale factor of 2 in the y direction would I do y/2 = (x+9)^3 + 2(x+9)^2 + 10, which gives me

    2(x+9)^3 + 4(x+9)^2 + 20? I put it in desmos but it doesn't look right
    Why doesn't it look right?

    It has been stretched parallel y-axis by s.f. 2. All the stationary points are twice as high up than they were before. Everything in the y<0 region gets stretched twice downwards. Everything is as expected.
    Online

    12
    ReputationRep:
    Mad ting
    Posted on the TSR App. Download from Apple or Google Play
    • Thread Starter
    Online

    16
    ReputationRep:
    (Original post by RDKGames)
    Why doesn't it look right?

    It has been stretched parallel y-axis by s.f. 2. All the stationary points are twice as high up than they were before. Everything in the y<0 region gets stretched twice downwards. Everything is as expected.
    sh*tden thanks
    • Thread Starter
    Online

    16
    ReputationRep:
    (Original post by RedGiant)
    Mad ting
    yo i'm baffed with life. i'm not bad at maths you know but this graph stuff is confusing the hell out of me
    Online

    12
    ReputationRep:
    (Original post by amaraub)
    yo i'm baffed with life. i'm not bad at maths you know but this graph stuff is confusing the hell out of me
    I can see m8, what exam board are you with?

    And thx for follow ^^
    Posted on the TSR App. Download from Apple or Google Play
    • Thread Starter
    Online

    16
    ReputationRep:
    (Original post by RDKGames)
    Why doesn't it look right?

    It has been stretched parallel y-axis by s.f. 2. All the stationary points are twice as high up than they were before. Everything in the y<0 region gets stretched twice downwards. Everything is as expected.
    When reflecting in the y axis, do you times all the x by -1, and when reflecting in the x axis, do you times everything by -1?

    (Original post by RedGiant)
    I can see m8, what exam board are you with?

    And thx for follow ^^
    edexcel, u?

    following so i can dm for maths and chat u up
    Online

    12
    ReputationRep:
    (Original post by amaraub)
    edexcel, u?

    following so i can dm for maths and chat u up
    I'm on edexcel as well (done chapters 1-7 but don't know which bit of the spec this is)
    Posted on the TSR App. Download from Apple or Google Play
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by amaraub)
    When reflecting in the y axis, do you times all the x by -1, and when reflecting in the x axis, do you times everything by -1?
    Same principles as above. Reflection in the y-axis means x \mapsto (-x) and reflection in the x-axis means y \mapsto (-y).

    Wasn't this covered in GCSE reflections of graphs or something...?
    • Thread Starter
    Online

    16
    ReputationRep:
    (Original post by RDKGames)
    Same principles as above. Reflection in the y-axis means x \mapsto (-x) and reflection in the x-axis means y \mapsto (-y).

    Wasn't this covered in GCSE reflections of graphs or something...?
    Yeah it probably was but I didn't really listen during GCSE lessons :/ Thanks though

    (Original post by RedGiant)
    I'm on edexcel as well (done chapters 1-7 but don't know which bit of the spec this is)
    This is chapter 4. I have 2 teachers, and 1 of them is really good, but the other is a total d*ck and hates me. Unfortunately the d*ck is the one that covered chapter 4, but we barely did any exercises in the textbook, and now I'm trying to do all of them and the 2 tasks on maths genie and really try to understand each concept. I''ve never really listened with graphs as in my old school we did graphs in year 10 with some dead teacher so in year 11 we just skipped ahead with our new better teacher.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Did TEF Bronze Award affect your UCAS choices?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.