Final answer:
The vertex of the quadratic function y = 1/2(x - 6)^2 + 1, which is possibly the intended function from the question, is (6, 1).
Step-by-step explanation:
The student is asking about the vertex of a quadratic function represented by the equation y = 1/2(12x - 61) + 1. To find the vertex of a quadratic function in the form y = ax^2 + bx + c, you can use the vertex formula, which is (-b/2a, f(-b/2a)), where f(x) represents the quadratic function. However, the equation provided appears to be incorrectly formatted. If we assume the correct equation is y = 1/2(x - 6)^2 + 1, which resembles vertex form (y=a(x-h)^2 + k), then the vertex is simply the point (h, k). In this case, the vertex would be (6, 1).