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

    0
    ReputationRep:
    another question im stuck on........
    the curve C with equation y=x^2 - 6x + 18 meets the y-axis at P and has a minimum point at Q.
    sketch the graph of C, showing the coordinates of P and Q...
    how would you work these 2 points out and what would the graph look like?
    thanks if you could help
    • PS Helper
    Offline

    14
    If you have a point x-coordinate must be zero, so to find P you need to substitute x=0 into the equation. This then gives P=(0,y), where y is to be found.

    To find the minimum point you need to complete the square. Say you have y=(x+a)^2+b. Then since any square number is always greater than or equal to zero, we have y \ge b, and it is only equal to b when (x+a)^2=0, which happens when x=-a, and so the minimum point must be at (-a,b). See if you can apply this to your problem.

    When you plot the graph, you need to plot the minimum point (which is where the curve 'bends' back upwards), and the point where it crosses the y-axis. If you're feeling keen you can also find where it crosses the x-axis (i.e. the roots of the polynomial), and then you have more than enough information to make a convincing sketch.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by nuodai)
    If you have a point x-coordinate must be zero, so to find P you need to substitute x=0 into the equation. This then gives P=(0,y), where y is to be found.

    To find the minimum point you need to complete the square. Say you have y=(x+a)^2+b. Then since any square number is always greater than or equal to zero, we have y \ge b, and it is only equal to b when (x+a)^2=0, which happens when x=-a, and so the minimum point must be at (-a,b). See if you can apply this to your problem.

    When you plot the graph, you need to plot the minimum point (which is where the curve 'bends' back upwards), and the point where it crosses the y-axis. If you're feeling keen you can also find where it crosses the x-axis (i.e. the roots of the polynomial), and then you have more than enough information to make a convincing sketch.
    thanks for the help i understand it all but i dont know what x^2 - 6x + 18 is in the form (x+a)^2+b
    sorry but i cant really remember how to do it!
    thanks if you could help further
    • PS Helper
    Offline

    14
    (Original post by Jay1012)
    thanks for the help i understand it all but i dont know what x^2 - 6x + 18 is in the form (x+a)^2+b
    sorry but i cant really remember how to do it!
    thanks if you could help further
    x^2-6x+18 isn't in the form (x+a)^2+b, but you can put it in that form. Do you know how to complete the square?
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by nuodai)
    x^2-6x+18 isn't in the form (x+a)^2+b, but you can put it in that form. Do you know how to complete the square?
    i just tried and got (x-3)^2 + 9 but i think that's wrong.
    no i dont really know, can you help ? please
    • PS Helper
    Offline

    14
    (Original post by Jay1012)
    i just tried and got (x-3)^2 + 9 but i think that's wrong.
    no i dont really know, can you help ? please
    Why do you think it's wrong? It looks right to me.

    So if (x-3)^2+9=(x+a)^2+b then what is a? What is b? So what are the coordinates of the minimum point?
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by nuodai)
    Why do you think it's wrong? It looks right to me.

    So if (x-3)^2+9=(x+a)^2+b then what is a? What is b? So what are the coordinates of the minimum point?
    so the minimum point is (-3, 9) ?

    or you said it is (-a, b)
    which would be (--3, 9)
    = (3, 9)

    so is it (-3, 9) or (3, 9) ?????
    • PS Helper
    Offline

    14
    (Original post by Jay1012)
    so the minimum point is (-3, 9) ?

    or you said it is (-a, b)
    which would be (--3, 9)
    = (3, 9)

    so is it (-3, 9) or (3, 9) ?????
    I could just give you the answer but you'll probably learn something if I don't :p: What do you think the answer is? Try investigating. If you're still stuck I'll give you a prod in the right direction.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by nuodai)
    I could just give you the answer but you'll probably learn something if I don't :p: What do you think the answer is? Try investigating. If you're still stuck I'll give you a prod in the right direction.
    i really dont know please help
    • PS Helper
    Offline

    14
    (Original post by Jay1012)
    i really dont know please help
    Well what writing the coordinate (p,q) means is that x=p and y=q.

    What happens when you evaluate y=(x-3)^2+9 when x=-3,y=9? What about when x=3,y=9?

    What about if you just put x=3 or x=-3 to find the resulting value of y? Which of the two resulting values of y is bigger?

    So which do you think is the minimum value?
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by nuodai)
    Well what writing the coordinate (p,q) means is that x=p and y=q.

    What happens when you evaluate y=(x-3)^2+9 when x=-3,y=9? What about when x=3,y=9?

    What about if you just put x=3 or x=-3 to find the resulting value of y? Which of the two resulting values of y is bigger?

    So which do you think is the minimum value?
    i think it's (-3, 9) ??????????
    • PS Helper
    Offline

    14
    (Original post by Jay1012)
    i think it's (-3, 9) ??????????
    Are you guessing or are you following my guidance? Show some of your working instead of giving final answers, then I can see if/where you're going wrong.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by nuodai)
    Are you guessing or are you following my guidance?
    no i read what you said and i think it's (-3, 9) ??
    • PS Helper
    Offline

    14
    (Original post by Jay1012)
    no i read what you said and i think it's (-3, 9) ??
    Why do you think that? Show your working. I'll show you where you're going wrong.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by nuodai)
    Why do you think that? Show your working. I'll show you where you're going wrong.
    i really dont know........... doesn't matter thanks for the help anyway
 
 
 
  • 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.