Question

The seat on a swing set sits 3 feet off the ground. The chains that are attached to the seat are 74 inches long. Suppose you were to swing: the path of the swing forms a parabola. Interpret the y-value of the vertex, in terms of the context.(1 point)Responsesy=all real numbersy equals all real numbersy=3y equals 3y≤74y less-than-or-equal-to 74y≤3y less-than-or-equal-to 3

Answer 1

In this context, the vertex of the parabola represents the highest point that the swing can reach during its motion. Since the seat of the swing is 3 feet off the ground, and considering the swing's chains are 74 inches (or approximately 6.17 feet) long, the maximum height the seat can reach is at its vertex.

Therefore, the y-value of the vertex, in terms of the context, specifically represents the maximum height of the swing above the ground level. Since the seat of the swing is already 3 feet off the ground, the relevant interpretation is:

y = 3

This means the swing seat can go a maximum of 3 feet high when at rest.

Thus, the response is: y = 3