Final answer:
The vertex of the given quadratic function f(x) = x^2 - 2x - 8 is (1, -9).
Step-by-step explanation:
The given function is f(x) = x2 - 2x - 8. To find the vertex and intercepts, we can use the formula x = -b/2a to find the x-coordinate of the vertex. In this case, a = 1, b = -2, and c = -8. Plugging these values into the formula, we get x = -(-2) / (2*1) = 1. So the x-coordinate of the vertex is 1. To find the y-coordinate, we substitute x = 1 into the function and evaluate it, giving us f(1) = 12 - 2*1 - 8 = 1 - 2 - 8 = -9. Therefore, the vertex of the function is (1, -9).