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≤74y less-than-or-equal-to 74y=all real numbersy equals all real numbersy=3y equals 3y≤3

Answer 1

To interpret the y-value of the vertex in the context of the swing set, let's analyze the given information:

• The seat of the swing is 3 feet off the ground. This indicates that the maximum height of the swing seat, when it is at its vertex (the highest point), is 3 feet.

• The chains are 74 inches long, which is equal to 6.17 feet (since 74 inches / 12 inches per foot = 6.17 feet). The maximum length of the chain dictates how far the swing can extend, but in terms of height, the most relevant point is where the swing seat is directly at its highest point, which is 3 feet off the ground.

In this case, the y-value of the vertex corresponds to the maximum height the swing can achieve relative to the ground. Therefore, since the swing seat is 3 feet off the ground, the y-value of the vertex is 3.

Thus, the correct interpretation is:

y = 3.