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Math Help - parabola equation

  1. #1
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    parabola equation

    Hi everyone,
    I have a simple question but I can't solve it
    what is the intersection point between these two parabola
    y=x^2
    and
    x=4y-y^2

    Thanks for any kind of help.
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  2. #2
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by rosana View Post
    Hi everyone,
    I have a simple question but I can't solve it
    what is the intersection point between these two parabola
    y=x^2
    and
    x=4y-y^2

    Thanks for any kind of help.
    y=(4y-y^2)^2

    Now expand and solve
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  3. #3
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    when I expand the equation y=(4y-y^2)^2
    it will be
    y^4-8y^3+16y^2-y=0
    I know that y=0
    but what about the other solution of the equation?
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  4. #4
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by rosana View Post
    when I expand the equation y=(4y-y^2)^2
    it will be
    y^4-8y^3+16y^2-y=0
    I know that y=0
    but what about the other solution of the equation?
    Use the Intermediate Value Theorem
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  5. #5
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    I know the meaning of intermediate value theorem is that there is apoint c in interval [a,b] for a function f verifying
    f'(c)=(f(b)-f(a))/(b-a)

    How is this related to the solution of the equation?
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  6. #6
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by rosana View Post
    I know the meaning of intermediate value theorem is that there is apoint c in interval [a,b] for a function f verifying
    f'(c)=(f(b)-f(a))/(b-a)

    How is this related to the solution of the equation?

    College Algebra Tutorial on Zeros of Polynomial Functions, Part II
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