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Help Identifying x-intercepts of quadratic functions

  1. Feb 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Identify the vertex and x-intercept(s) of the quadratic function algebraically.



    2. Relevant equations

    f(x) = 1/2x^2 - 4

    1/2 Is the coefficent if its not clear.



    3. The attempt at a solution

    Ok I do not need help finding the vertex I have already got that, I need help factoring it out to find the x-intercepts.

    Here is my attempt

    0 = 1/2x^2 - 4
    0 = 1/2 (x^2 - 8)

    That is as far as I can factor it, I am terrible at factoring these and I actually have a way easier time factoring trinomials and polynomials.

    Could you please explain how I am to factor farther and how am I supposed to solve for the x-intercepts after its all factored. I have even looked all over the internet for a good factoring tutorial guide but I just cannot even understand them.

    Thanks
     
    Last edited: Feb 9, 2009
  2. jcsd
  3. Feb 9, 2009 #2
    There is no need to worry that much about factoring. You have

    [tex]\frac{1}{2}x^{2}-4=0.[/tex]​

    Simply solve for x to obtain the intercept.
     
  4. Feb 10, 2009 #3

    HallsofIvy

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    Science Advisor

    I believe that was what he was trying to do! Kalzar89, there is no need to factor.
    [itex](1/2)x^2- 4= 0[/itex]
    [itex] (1/2)x^2= 4[/itex]
    [itex]x^2= 8[/itex]
    and take the square root of both sides.
    [itex]x= \pm\sqrt{8}= \pm \sqrt{(4)(2)}= \pm 2\sqrt{2}[/itex]
     
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