How do you find the x and y axes of a function without the graph?

Nov 14, 2016

(see below)

Explanation:

It is unclear what you are looking for here (especially since this appears under "Rotations of a Conic Section").

The X-axis is the collection of points for which $y = 0$.
If you are looking for the x-intercept, it is
$\textcolor{w h i t e}{\text{XXX}} \left(\hat{x} , 0\right)$ where $f \left(\hat{x}\right) = 0$
$\textcolor{w h i t e}{\text{XXX}}$i.e. you need to solve your function for when the function equals zero.

The Y-axis is the collection of points for which $x = 0$
If you are looking for the y-intercept, it is
$\textcolor{w h i t e}{\text{XXX}} \left(0 , f \left(0\right)\right)$