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)

Question

Responses

y=
all real numbers
y equals all real numbers

y≤74
y less-than-or-equal-to 74

y=3
y equals 3

y≤3

Answer 1

To interpret the y-value of the vertex in the context of the swing, we need to understand what the vertex represents in this scenario.

The vertex of a parabola formed by the swing's path is the highest point of the swing's trajectory. In this case, the seat of the swing is 3 feet off the ground, which represents the lowest point of the swing when it is at rest.

The longest chain length is 74 inches, which is approximately 6 feet (since 74 inches is 6 feet and 2 inches). When the swing is at its highest point, the swing's seat will be at its maximum height.

Given the situation:

1. The lowest y-value when the seat is hanging down is 3 feet.
2. The chain's length suggests the swing can reach heights above 3 feet when in motion.

Thus, if we interpret the vertex in the context of the swing's path, the y-value representing the lowest point (where the vertex is) corresponds to y = 3 feet.

So the correct interpretation of the y-value of the vertex in this context is:

y = 3 (y equals 3).