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Math Help - simple question about dilations

  1. #1
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    simple question about dilations

    27x^2- is this a dilation of a factor of 27 from the x intercept and a dilation of 1/27 from the y intercept?
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    Quote Originally Posted by chaneliman View Post
    27x^2- is this a dilation of a factor of 27 from the x intercept and a dilation of 1/27 from the y intercept?
    g(x) = 27 x^2 can be considered a transformation of f(x) = x^2 in two different ways:

    1. g(x) = 27 f(x)\, - dilation by a factor of 27 in the vertical direction, that is, from the x-axis.

    2. g(x) = f(\sqrt{27}x)\, - dilation by a factor of \frac{1}{\sqrt{27}} = \frac{1}{3\sqrt{3}} in the horizontal direction, that is, from the y-axis.

    1. is the way that most folk would think of it.
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    where did the square root come form? for 1/square root 27
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    Quote Originally Posted by chaneliman View Post
    where did the square root come form? for 1/square root 27
    27x^2 = (\sqrt{27} x)^2.

    If the second way bothers you, forget you ever saw it. As I said, the first way is how most folk would think of it and is undoubtedly how your teacher would think of it.
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