Use the image to answer the question.

Question

An open, downward facing parabola is graphed on a coordinate plane. The x-axis ranges from negative 2 to 5 in increments of 1. The y-axis ranges from negative 1 to 16 in increments of 2.

Interpret the following quadratic function model and graph given the following context. A volleyball is served into the air at 26 ft./sec
from a height of 4.5 ft. The quadratic equation represents the height of the ball over time and in seconds. The graph illustrates this path where x represents the time in seconds and f(x)
represents the height in feet. Approximately how long does it take for the volleyball to reach maximum height?

(1 point)
Responses

approximately 5 seconds
approximately 5 seconds

approximately 2 seconds
approximately 2 seconds

approximately 0.85 seconds
approximately 0.85 seconds

approximately 15 seconds

Answer 1

To find the time it takes for the volleyball to reach maximum height, we typically look for the vertex of the parabola represented by the quadratic function. For the quadratic function \( f(x) = ax^2 + bx + c \), the x-coordinate of the vertex, which gives the time at maximum height, can be calculated using the formula:

\[ x = -\frac{b}{2a} \]

However, since we do not have the specific quadratic equation, the height you provided indicates that the ball is served into the air and would typically reach its maximum height quite soon after being served.

Given the response options and typical behavior of quadratics in similar scenarios, the answer would most likely be:

approximately 2 seconds.

This is common for projectile motion where maximum height is reached relatively quickly after the initial serve.