college algebra

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On the graph, plot all relevant points for y=x^2-4x+y^2-2y+8. Then give the equation for a graph that shifts down 1 unit and to the right 2 units. If it is a function, give its domain and range.
Thank you!!

  • college algebra -

    I find it odd that your textbook stated the equation in this unsimplified form, since we could combine the two y terms to read

    x^2 - 4x + y^2 - 3y + 8 = 0

    From that form I recognize a circle.
    let's complete the square:
    x^2 - 4x + 4 + y^2 - 3y + 9/4 = -8+4+9/4
    (x-2)^2 + (y-3/2)^2 = 1/4

    so centre is (2,3/2) and radius is 1/2

    we want to move this 1 unit down and 2 to the right, so
    (x-2-2)^2 + (y-3/2+1)^2 = 1/4
    (x-4)^2 + (y-1/2)^2 = 1/4

    expand it if you will
    new centre is (4,1/2), radius is still 1/2

  • college algebra -

    It was on a test. I think it was written like that to trick us. Normally I don't have a problem with math, but this teacher is pretty tricky! I really appreciate all of your help=;)

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