Find the critical points alpha and beta by solving the given quadratic equation.

The project's progress is modeled by the equation:

We can factor this quadratic equation:

The roots are $x = 2$ and $x = 8$.
Let $\alpha = 2$ and $\beta = 8$.

The inverse of $\alpha$ is $\frac{1}{\alpha}$.

The inverse of $\beta$ is $\frac{1}{\beta}$.

The inverses of the critical points are $\boxed{\frac{1}{2} \text{ and } \frac{1}{8}}$.

The new critical points (inverse critical points) are $\frac{1}{2}$ and $\frac{1}{8}$.

A quadratic equation with roots $r_1$ and $r_2$ can be written as $y^2 - (\text{sum of roots})y + (\text{product of roots}) = 0$.

To eliminate fractions, multiply the entire equation by the least common multiple of the denominators (16):

The equation that models these inverse critical points is $\boxed{16y^2 - 10y + 1 = 0}$.