Final answer:
The student's question about finding the values of a and b for continuity of a function f is slightly unclear due to insufficient details about f(x). The provided detail involving a quadratic equation suggests a different problem, thus without more information, the correct values of a and b cannot be identified.
Step-by-step explanation:
The student asked about finding the values of a and b that make the function f continuous everywhere. To address continuous functions in a mathematical context, we consider the scenarios where the function needs to be evaluated to maintain continuity. Often a function that's piecewise or has conditional definitions needs to be evaluated at specific points to ensure the continuity of the function across its entire domain.
Given the information about horizontal lines and the restricted domain for x (from 0 to 20), it sounds like we're dealing with a function that's constant over that interval. However, the provided details about a quadratic equation with constants a=1.00, b=10.0, and c=-200 are likely relevant to another problem involving finding roots using the quadratic formula. Therefore, without more specific information about the function f(x), we cannot determine which values of a and b will ensure continuity.