Final answer:
The function f(x) = (x + 5)^2 has an absolute minimum value of 25 at x = 0 and an absolute maximum value of 625 at x = 20 within the domain 0 ≤ x ≤ 20.
Step-by-step explanation:
To identify the function's extreme values within the given domain and determine which values are absolute, we need to analyze the function f(x) = (x + 5)^2. This function is a parabola that opens upwards, and its vertex represents the minimum point, since there are no maximum points for this function because it extends to infinity as x increases or decreases.
The vertex of this function is at the point (-5, 0). The given domain, however, is from 0 ≤ x ≤ 20, which does not include the vertex. Within this domain, the minimum occurs at the left endpoint x = 0 because the function is increasing on this interval. Plugging this value into the function, we get f(0) = (0 + 5)^2 = 25. Since this function continually increases, the maximum value within the domain occurs at the right endpoint, x = 20. Therefore, f(20) = (20 + 5)^2 = 625.
Thus, the function has an absolute minimum of 25 at x = 0 and an absolute maximum of 625 at x = 20 within the given domain.