to begin a football game, a kicker has to kick off the football follow the path H(x) = -1/30x(x-61), where h(x) is the height of the football game and x is the horizontal distance it has traveled in yards.
To begin a football game, a kicker has to kick off the football, following the path described by the function:
H(x) = -(1/30)x(x-61)
Here, H(x) represents the height of the football game, and x represents the horizontal distance it has traveled in yards.
The equation H(x) = -(1/30)x(x-61) is a quadratic function in the form of h(x) = ax² + bx + c, where a = -(1/30), b = 0, and c = 0.
The graph of this quadratic function represents the path of the football in the air. The vertex of the parabola represents the highest point the football reaches during its trajectory.
To find the highest point, or vertex, of the parabola, we can determine the x-coordinate using the formula:
x-coordinate of vertex = -b / (2a)
= -0 / (2 * (-1/30))
= 0
Since the x-coordinate of the vertex is 0, the football reaches its highest point at the start, when it is kicked off.
To find the y-coordinate of the vertex, we substitute the x-coordinate into the original function:
y-coordinate of vertex = H(x-coordinate of vertex)
= H(0)
= -(1/30)(0)(0-61)
= 0
Therefore, the highest point the football reaches during its path is at (0,0), indicating that the football starts at ground level when it is kicked off.
The graph of the function would be a downward-opening parabola, starting from ground (y=0) and reaching its lowest point at x=30. Then, it rises again, reaching ground again at x=61.