1. ## 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?

2. 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.

3. where did the square root come form? for 1/square root 27

4. 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.