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Use algebra to find the x and y intercepts , for a quadratic equation

  1. Jul 7, 2012 #1
    1. The problem statement, all variables and given/known data

    Use algebra to find the x-intercepts and y-intercept of The graph of y=-x^2/5+x/5+6
    this is a parabola.

    2. Relevant equations
    y=-x^2/5+x/5+6


    3. The attempt at a solution
    Find the y-intercept , which is substitute 0=x into the equation to find the answer , done that .
    The problem I have is where to start to find the x-intercept , I know that y=0 so I now have x^2/5+x/5+6=0 , but believe I can't now factorise this equation and will have to first clear the fractions first . Is this the right place to start.
     
    Last edited: Jul 7, 2012
  2. jcsd
  3. Jul 7, 2012 #2

    Sounds a good place to me. What do you then get? Have you learnt e.g. completing the square, or the quadratic formula yet?
     
  4. Jul 7, 2012 #3
    Not answered the question yet ,and not done them yet they are coming up in the section.
    Will try and find the answer in a bit and post my results .
     
  5. Jul 7, 2012 #4
    Hint: since one side of the equation=0, you can easily multiply both sides by 5, and then -1...
     
  6. Jul 7, 2012 #5

    Curious3141

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    Homework Helper

    Note that you've dropped the minus sign on the coefficient of the [itex]x^2[/itex] term the last time you wrote that (in bold). That minus sign is all-important. Without that, you don't have an x-intercept!
     
  7. Jul 7, 2012 #6
    yeah thank you for that i will remember the minus sign
     
  8. Jul 7, 2012 #7

    HallsofIvy

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    Once you have done what e^pi i + 1= 0 suggested, multiplying the entire equation by -5, you will have a quadratic equation with integer coefficients that is easy to factor.
     
  9. Jul 7, 2012 #8
    Ah right think I have it now , multiply by the least common denominator, which is 5, which leaves me with -x^2+x-30=0 and the by -1 to get x^2-x-30=0 and then factor to get (x+5)(x-6).
    Thank you everyone
     
  10. Jul 7, 2012 #9

    HallsofIvy

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    No, you get -x^2+ x+ 30 but then your next is correct:
    Yes, that is correct.
     
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