Final answer:
The vertex of the function f(x) = 2(x − 5)^2 + 8 is determined from its vertex form and is at the point (5, 8). The vertex is given by the point (h, k) in the general vertex form of a quadratic function which is f(x) = a(x − h)^2 + k for this function.
Step-by-step explanation:
To determine the vertex of the function f(x) = 2(x − 5)^2 + 8, we should recognize that this function is in vertex form, where the general form is f(x) = a(x − h)^2 + k. For our function, a = 2, h = 5, and k = 8. In this format, the vertex of the parabola described by the quadratic equation is directly given as (h, k).
The vertex form makes it easy to identify the vertex without needing additional calculations.
Therefore, the vertex of the function given is at the point (h, k) = (5, 8).
Note that even though other options are provided, such as (8, −5), (8, 5), and (−5, 8), none of these represent the correct vertex of the function based on the vertex form given. The correct answer is (5, 8) since it corresponds with the values of h and k in the vertex form of the quadratic function we are examining.