Final answer:
Option B reveals the minimum number of miles, in millions, US passengers traveled on a train for the period of 1970 to 2000, which is 4899 million miles because it is in vertex form and indicates the lowest point on the parabola.
Step-by-step explanation:
The student is asking which equivalent form reveals the minimum number of miles, in millions, US passengers traveled on a train for the period of 1970 to 2000. To find the minimum value given by a quadratic function, we should look for the form that represents the vertex of a parabola. The vertex form of a quadratic function is given by M(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola, and a indicates the direction and width of the parabola.
In this case, the only two quadratic functions in vertex form are options B and D. Looking at option B, since 'a' is positive (5), this means the parabola opens upwards, and the vertex (16, 4899) represents the minimum number of miles traveled. Similarly, option D has the same upward direction (since 'a' is also 5), but with a higher constant value (6435), meaning the minimum value would be higher than that of option B.
Therefore, option B reveals the minimum number of miles, in millions, US passengers traveled on a train for the period of 1970 to 2000, which is 4899 million miles.