Final answer:
The maximum height of the ball, based on the given quadratic equation, is found to be 86 units, and not any of the provided choices. The calculation involves finding the vertex of the parabola represented by the equation, which is not matched by the answer choices, indicating a possible error.
Step-by-step explanation:
To find the maximum height of the ball from the equation y = -1/20x^2 + 4x + 6, we need to determine the vertex of this parabola, as the coefficient of the x^2 term is negative which implies that the parabola opens downwards. Therefore, the vertex of this parabola represents the maximum height of the ball. The x-coordinate of the vertex can be found using the formula -b/2a, where a is the coefficient of x^2, and b is the coefficient of x. In this case, a = -1/20 and b = 4.
Calculating the x-coordinate: x = -b/2a = -4/(2*(-1/20)) = -4/(-1/10) = 40. Substituting x = 40 back into the original equation to find y yields the maximum height: y = -1/20*40^2 + 4*40 + 6.
Simplifying: y = -1/20(1600) + 160 + 6 = -80 + 166 = 86. Thus, the maximum height of the ball is 86 units, and none of the answer choices A) 4 units B) 6 units C) 8 units D) 10 units are correct. The correct answer should be 86 units, indicating a possible typo or error in the given choices.