Sometimes, the method of least squares can be used for problems that, in principle, could not be addressed by the method.
For example, let's suppose we want to find $a$ and $b$ in order to fit the function $\frac{1}{{a + bx}}$ to the points $(x_i, y_i)$ by minimizing $$min\frac{1}{2}\sum_{i=1}^m (\frac{1}{a + bx_i} - y_i)^2$$
This minimization is not in a form that the method of least squares can solve. However, an idea is to find a transformation $T$ such that $$min\frac{1}{2}\sum_{i=1}^m [T(\frac{1}{a + bx_i}) - T(y_i)]^2$$ is a problem of least squares. In the given case, if we use $T(x) = \frac{1}{x}$, we will have the minimization of $$min\frac{1}{2}\sum_{i=1}^m (a + bx_i - \frac{1}{y_i})^2$$
where we can apply the method of least squares.
Find appropriate transformations for the following functions:
a) $f(x) = ae^{bx}$
b) $f(x) = \frac{1}{{a + bx + cx^2}}$
So, for letter A, I used the transformation $T(x) = \ln(x)$, which provides the desired result. However, in letter B, I'm uncertain about the next steps. How can we transform a quadratic function into a linear function so that we can apply the least squares method?