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.