Function Model Selection and Assumption Articulation Practice Test

Data from an experiment shows a relationship where the output variable increases to a single maximum value and then decreases, appearing to be symmetric. Both a quadratic and a quartic ($$4^{th}$$ degree) polynomial model fit the data well. In the absence of a theoretical reason to prefer one over the other, why might a researcher choose the quadratic model?

The height $$h$$, in meters, of a ball thrown upwards from a building is modeled by the function $$h(t) = -4.9t^2 + 20t + 50$$, where $$t$$ is the time in seconds after the ball is thrown. Which of the following describes a necessary restriction on the domain of the function for this model to be physically realistic?