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Math Help - Trying to solve for y here....

  1. #1
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    Trying to solve for y here....

    I'm working on a calculus problem, but I'm stuck with something algebraically:

    x = y^2-7y

    I'm trying to solve for y so I can graph it. I started by factoring y:

    x = y(y-7)

    But that's as far as I can get. If I divide both sides by y, that still leaves me with x/y = y-7. The extra y on the right side of the equation is stumping me and I can't figure out how to get rid of it. Any ideas?
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  2. #2
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    This is a quadratic equation: y^2-7y-x=0. Depending on x, it may have zero, one or two solutions, which are given by the standard formula for the roots of a quadratic equation.
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  3. #3
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    Quote Originally Posted by bobbooey View Post
    I'm working on a calculus problem, but I'm stuck with something algebraically:

    x = y^2-7y

    I'm trying to solve for y so I can graph it. I started by factoring y:

    x = y(y-7)

    But that's as far as I can get. If I divide both sides by y, that still leaves me with x/y = y-7. The extra y on the right side of the equation is stumping me and I can't figure out how to get rid of it. Any ideas?
    complete the square ...

    x + \frac{49}{4} = y^2 - 7y + \frac{49}{4}

    x + \frac{49}{4} = \left(y - \frac{7}{2}\right)^2

    x = \left(y - \frac{7}{2}\right)^2 - \frac{49}{4}

    vertex of the parabola is at \left(-\frac{49}{4} , \frac{7}{2}\right) and the parabola opens up to the right.
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  4. #4
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    My issue is that I need to find where the two lines intersect (In Quadrant II)

    x = y^2-7y
    x = 2y-y^2

    After about 30 minutes of brute forcing it, I figured out that that they intersect at (-11.25,4.5) but does an easier method exist mathematically for determining that?
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  5. #5
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    Quote Originally Posted by bobbooey View Post
    My issue is that I need to find where the two lines intersect (In Quadrant II)

    x = y^2-7y
    x = 2y-y^2

    After about 30 minutes of brute forcing it, I figured out that that they intersect at (-11.25,4.5) but does an easier method exist mathematically for determining that?

    solve y^2-7y= 2y-y^2
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