Final answer:
To find the maximum height of the ball, the vertex of the parabola y = -0.2x^2 + 2.4x + 2 is calculated. The maximum height, 9.2 meters, is found by substituting the x-value of the vertex back into the equation. The provided options do not match the calculated maximum height.
Step-by-step explanation:
To determine the maximum height of the ball using the equation y = -0.2x^2 + 2.4x + 2, we need to find the vertex of the parabola represented by the equation, which occurs at the axis of symmetry. The axis of symmetry can be found using the formula x = -b/(2a) when the quadratic equation is in the form y = ax^2 + bx + c.
For our equation, a = -0.2 and b = 2.4. Plugging these into the axis of symmetry formula, we get x = -2.4/(2 * -0.2) = 6 meters. This is the horizontal distance at which the ball reaches its maximum height. To find the maximum height, we plug x = 6 into the original equation:
y = -0.2(6)^2 + 2.4(6) + 2 = -7.2 + 14.4 + 2 = 9.2 meters.
Therefore, the maximum height of the ball is 9.2 meters, which is not one of the options provided. It seems there may have been an error in the options given or the equation provided.