Answer: 49.2 feet
Explanation:
The given equation h = -16t^2 + 56t represents the height of a football kicked by Lauren as a function of time t in seconds.
In the context of the problem, the vertex of the parabolic function (-16t^2 + 56t) represents the point at which the football reaches its maximum height. The vertex of a parabola is the point where the function reaches its highest or lowest value, and it is given by the coordinates (h, t) in this case.
Interpreting the coordinates of the vertex in context, the h-coordinate represents the maximum height of the football, while the t-coordinate represents the time at which the football reaches that maximum height. So, if we determine the vertex of the given function, we can interpret the maximum height and the time it occurs.
The formula for the x-coordinate (t) of the vertex of a quadratic function in the form y = ax^2 + bx + c is given by t = -b/2a. Comparing this with the given equation, we can identify that a = -16 and b = 56.
Plugging in the values of a and b into the formula, we get:
t = -56 / (2 * -16)
t = -56 / -32
t = 1.75
So, the t-coordinate of the vertex is 1.75 seconds, which represents the time at which the football reaches its maximum height.
To find the h-coordinate of the vertex, we can substitute the value of t we found (1.75) into the given equation:
h = -16(1.75)^2 + 56(1.75)
h = -16(3.0625) + 98
h = -48.8 + 98
h = 49.2
So, the h-coordinate of the vertex is 49.2, which represents the maximum height of the football in feet.
In conclusion, the coordinates of the vertex (49.2, 1.75) in the given context represent the maximum height (49.2 feet) of the football and the time (1.75 seconds) at which the football reaches its maximum height after being kicked by Lauren.