The question asks for the formula used to calculate the \(VO_2 \text{ max}\) in the Cooper 12-minute Run/Walk Test. This test estimates the physical fitness of an individual by measuring how far they can run/walk in 12 minutes. The \(VO_2 \text{ max}\) is a measure of the maximum amount of oxygen an individual can utilize during intense exercise, expressed in milliliters of oxygen per kilogram of body weight per minute (ml.kg^-1.min^-1).

Let's evaluate the given options:

1. Option 1: \(VO_2 \text{ max (ml.kg}^{-1}\text{.min}^{-1}) = 3.5 + (438 \div \text{time in minutes})\). 
   This does not pertain to the Cooper Test; it's more aligned with other fitness tests.
2. Option 2: \(VO_2 \text{ max (ml.kg}^{-1}\text{.min}^{-1}) = (\text{Distance} - 0.3138) \div 0.0278\). 
   This is the correct formula for the Cooper 12-minute Run/Walk Test. It calculates the \(VO_2 \text{ max}\) based on the distance covered in meters during the 12-minute period.
3. Option 3: \(VO_2 \text{ max (ml.kg}^{-1}\text{.min}^{-1}) = 108.94 - 8.41 (\text{time}) - 0.38 (\text{time}^2)\). 
   This is a regression formula unrelated to the Cooper Test.
4. Option 4: \(VO_2 \text{ max (ml.kg}^{-1}\text{.min}^{-1}) = -32.678 + 6.592 (\text{maximal speed})\). 
   This formula estimates \(VO_2 \text{ max}\) based on maximum speed, not applicable here.

The Cooper Test requires you to measure the distance covered in meters after running for 12 minutes, and then apply the formula from Option 2 to calculate \(VO_2 \text{ max}\).

Conclusion: Option 2 is the correct formula used for calculating the \(VO_2 \text{ max}\) in the Cooper 12-minute Run/Walk Test.