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Math Help - parabola intersection

  1. #1
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    Question parabola intersection

    Using a graphing utility to find the point of intersection of the graphs. Then confirm your solution algebraically.
    y=3x^2
    y=2x^2-8x-15


    I did this graphically and I got (-3,27). How do I find the solution algebraically? I know it can't be hard, but I can't find it in the book.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by RenSully View Post
    Using a graphing utility to find the point of intersection of the graphs. Then confirm your solution algebraically.
    y=3x^2
    y=2x^2-8x-15


    I did this graphically and I got (-3,27). How do I find the solution algebraically? I know it can't be hard, but I can't find it in the book.
    Set y=y.

    In otherwords, solve

    3x^2=2x^2-8x-15

    for x.
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  3. #3
    Super Member Bacterius's Avatar
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    Can I say something though ? The question is wrong. You must give different letters to different equations. What you wrote means that for any x in R, 3x^2=2x^2-8x-15, which is wrong.

    So I would rather denote the two parabolas like this :

    y_1 = 3x^2
    y_2 = 2x^2 - 8x - 15

    Thus solve for y_1 = y_2, ... and Von Nemo already answered this I was just posting because of this (since solving x for y = y is absolutely meaningless, even though you understand it ... I mean let's talk math !)
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  4. #4
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    Thanks! I wish I were studying Nietzche/philosophy instead of Pre-calc. I am never going to remember all of this. Sigh...
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  5. #5
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Bacterius View Post
    ... and Von Nemo already answered this I was just posting because of this (since solving x for y = y is absolutely meaningless, even though you understand it ... I mean let's talk math !)
    The question - I believe - is that we are looking for \{(x,y)\in\mathbb{R}^2|3x^2=y\text{ and }2x^2-8x-15=y\}.

    Note that this implies that y=y.

    You are trying to distinguish between two parabolas, but notice the word "intersection". Once this word was tossed into the game, y became equal to y.
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  6. #6
    Super Member Bacterius's Avatar
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    Oh right, thanks for the explanation
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