• Feb 12th 2008, 08:22 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, 11:12 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?

$g(x) = 27 x^2$ 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.
• Feb 13th 2008, 12:09 AM
chaneliman
where did the square root come form? for 1/square root 27
• Feb 13th 2008, 12:44 AM
mr fantastic
Quote:

Originally Posted by chaneliman
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.