How to determine if an equation is linear or quadratic relationship?

Question

I have an equation of the form $y= \frac{v}{x^2} - \frac{1}{x}$. I can rewrite it as $y= vx^{-2} - x^{-1}$. I don't know if it's quadratic. Any suggestions on what this relationship would like?

Answer 1

$y=\frac{V}{x^2}-\frac{1}{x}$ is not quadratic. Quadradic equations have the form $y=ax^2+bx+c$. Depending on exactly what you're trying to do, you can solve for $y$ as such: $$y=\frac{V-x}{x^2}$$ so that $$yx^2=V-x$$

Make a column containing values for $y_n\times x_n^2$ and another for $x_n$. You can create a linear regression from the resulting data. The slope should be $-1$, while the y-intercept should equal $V$.

While simple, this may not be the best approach. There are ways to fit data to arbitrary equations like yours without linearizing it. Google "curve fitting in Excel" for some options.

EDIT: Your equation is also quadratic in $x^{-1}$. Form a quadratic regression of $y$ vs. $1/x$ and see what happens.