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 4.5ft.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?
The quadratic function model is:
f(x) = -16x^2 + 26x + 4.5
To determine how long it takes for the volleyball to reach maximum height, we need to find the x-value of the vertex of the parabola. The x-value of the vertex can be found using the formula:
x = -b / 2a
In this case, the coefficients of the quadratic function are a = -16 and b = 26, so:
x = -26 / (2*(-16))
x = -26 / -32
x = 0.8125
Therefore, it takes approximately 0.8125 seconds for the volleyball to reach maximum height.