text: • Feb 12th 2008, 07:22 PM
  chaneliman
  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?
  • Feb 12th 2008, 10:12 PM
  mr fantastic
  Quote:
  
  Originally Posted by chaneliman
  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?
  
  $\displaystyle g(x) = 27 x^2$ can be considered a transformation of $\displaystyle f(x) = x^2$ in two different ways:
  
  1. $\displaystyle g(x) = 27 f(x)\,$ - dilation by a factor of 27 in the vertical direction, that is, from the x-axis.
  
  2. $\displaystyle g(x) = f(\sqrt{27}x)\,$ - dilation by a factor of $\displaystyle \frac{1}{\sqrt{27}} = \frac{1}{3\sqrt{3}}$ in the horizontal direction, that is, from the y-axis.
  
  1. is the way that most folk would think of it.
  • Feb 12th 2008, 11:09 PM
  chaneliman
  where did the square root come form? for 1/square root 27
  • Feb 12th 2008, 11:44 PM
  mr fantastic
  Quote:
  
  Originally Posted by chaneliman
  where did the square root come form? for 1/square root 27
  
  $\displaystyle 27x^2 = (\sqrt{27} x)^2$.
  
  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.