Results 1 to 8 of 8

Math Help - Express 2x^2-28x+53

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    21

    Express 2x^2-28x+53

    Express 2x^2-20x+53 in the form 2(x-p)^2+q , where p and q are integers. not sure how to do this..

    i factorised it and got this
    2(x^2-10x)+53 plz help thx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by mike789 View Post
    Express 2x^2-20x+53 in the form 2(x-p)^2+q , where p and q are integers. not sure how to do this..

    i factorised it and got this
    2(x^2-10x)+53 plz help thx
    If:

    2(x-p)^2+q=2x^2-4px+2p^2+q=2x^2-20x+53

    then 4p=20, so p=5, and 2p^2+q=53 so q= .... ?

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Mar 2010
    Posts
    715
    Thanks
    2
    Quote Originally Posted by mike789 View Post
    i factorised it and got this
    2(x^2-10x)+53 plz help thx
    Good start! Now consider (x-5) = x-10x+25 which gives x-10x = (x-5)-25.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Jul 2009
    From
    Melbourne
    Posts
    272
    Thanks
    4
    This question is essentially asking you to express that quadratic in "turning point form". This is done by completing the square.

    Alternatively, you can "compare coefficients" described in CaptainBlack's post
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2011
    Posts
    2
    2x^2 - 20x + 53
    \equiv  2(x^2 - 10x) + 53 // Take the 2 outside of the brackets
    \equiv 2((x-5)^2 - 25) + 53 // Complete the square within the brackets
    \equiv 2(x-5)^2 - 50 + 53 // Take the -25 outside the brackets
    \equiv 2(x-5)^2 + 3 // Gather terms
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by jgv115 View Post
    This question is essentially asking you to express that quadratic in "turning point form". This is done by completing the square.

    Alternatively, you can "compare coefficients" described in CaptainBlack's post
    What I posted is completing the square, but done from first principles rather than remembering the algorithm, which I don't as it is a waste of brain space (same goes for a number of other things taught in common algebra and starting calculus, they are quicker to re-derive than to remember).

    CB
    Follow Math Help Forum on Facebook and Google+

  7. #7
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Quote Originally Posted by CaptainBlack View Post
    What I posted is completing the square, but done from first principles rather than remembering the algorithm, which I don't as it is a waste of brain space (same goes for a number of other things taught in common algebra and starting calculus, they are quicker to re-derive than to remember).

    CB
    Yes, yes. To CB you listen!
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    Joined
    Mar 2010
    Posts
    715
    Thanks
    2
    Quote Originally Posted by CaptainBlack View Post
    What I posted is completing the square, but done from first principles rather than remembering the algorithm, which I don't as it is a waste of brain space (same goes for a number of other things taught in common algebra and starting calculus, they are quicker to re-derive than to remember).
    If you are referring to remembering the formula for the coordinates of the turning point, I agree. But what I was hinting at post #3 doesn't really require remembering stuff at all.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Different way to express this set
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: February 21st 2011, 11:46 AM
  2. express in m and n
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: July 22nd 2010, 09:15 PM
  3. Express f(g(x))
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: April 20th 2009, 09:03 PM
  4. express in z=a+bi
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 14th 2009, 11:52 PM
  5. way to express ans
    Posted in the Trigonometry Forum
    Replies: 8
    Last Post: April 17th 2006, 07:00 AM

Search Tags


/mathhelpforum @mathhelpforum