To find the vertex of the quadratic function f(x) = (1/2)x^2, you can follow these steps: 1) Recall that the vertex of a quadratic function is given by the coordinates (h, k), where h represents the x-coordinate and k represents the y-coordinate. 2) The x-coordinate of the vertex, h, can be found using the formula h = -b / (2a), where a and b are the coefficients of the quadratic function in the standard form ax^2 + bx + c. 3) In this case, the coefficient of x^2 is (1/2), and the coefficient of x is 0 (since there is no x term in the function). Therefore, we have a = 1/2 and b = 0. 4) Substitute these values into the formula for h: h = -0 / (2 * (1/2)) = 0. 5) The y-coordinate of the vertex, k, can be found by substituting the value of h into the original function. So, we substitute x = 0 into f(x) = (1/2)x^2: f(0) = (1/2)(0)^2 = 0. 6) Therefore, the vertex of the function f(x) = (1/2)x^2 is (0, 0). The vertex is the point on the graph where the function reaches its minimum or maximum value, and in this case, since the coefficient of x^2 is positive, the vertex represents the minimum point of the function.