Question

Which quadratic function best fits this data?

Answer 1

The data has a peak at x=5, so we expect it to be modeled with a parabola that opens downward. That is the x² coefficient will be negative.

For x=1, the third choice gives a better approximation to (x, y) = (1, 32) than does the first choice. It is appropriate to choose

... y = -11.41x²+154.42x-143.9

_____

The quadratic regression function of a graphing calculator confirms this choice.