Final answer:
To find the maximum value of a quadratic function, we need to determine the coordinates of the vertex. By substituting the given values into the vertex formula, we find the vertex at (-1.46, 28.16). Evaluating the function at the vertex, we find that the maximum value is approximately 28.16.
Step-by-step explanation:
To determine the maximum value of a quadratic function, we need to identify the vertex of the parabola. The vertex of a quadratic function in the form ax^2 + bx + c is given by the coordinates (-b/2a, f(-b/2a)). In this case, the quadratic equation is 4.90t^2 + 14.3t - 20.0 = 0. We can find the vertex by substituting the values of a, b, and c into the vertex formula. After finding the vertex, we can determine the maximum value of the quadratic function by evaluating the function at that x-value.
By substituting the values of a, b, and c, we get t = -14.3 / (2 * 4.90) = -1.46. Substituting this value into the quadratic function, we get f(-1.46) = 4.90(-1.46)^2 + 14.3(-1.46) - 20.0 = 28.16. Therefore, the maximum value of the quadratic function is 28.16, which is closest to option A) 28.