Answer:
We can analyze this equation to determine information about the trajectory of the ball.
The equation of the ball's height is given by:
y = -1/14 x^2 + 6x + 3
where y is the height of the ball (in feet) and x is the time (in seconds).
The equation is in the form of a quadratic function, which means that the height of the ball will follow a parabolic path.
The coefficient of x^2 is negative (-1/14), which means that the graph of the function will open downwards, indicating that the ball will reach a maximum height and then fall back down.
The maximum height occurs at the vertex of the parabolic function, which can be found using the formula:
x = -b/2a
where a is the coefficient of x^2 and b is the coefficient of x. In this case, a = -1/14 and b = 6, so:
x = -6 / 2(-1/14) = 42
Therefore, the ball will reach its maximum height at 42/2 = 21 seconds.
Substituting x = 21 into the equation, we can find the maximum height:
y = -1/14 (21^2) + 6(21) + 3 = 120 feet
Therefore, the ball will reach a maximum height of 120 feet after 21 seconds, and then fall back down, following the same parabolic path.
Explanation: