Final answer:
The vertex of the quadratic function f(x) = x² - 12x + 5 is at (6, -31), which can be found using the vertex formula and substituting the values into the function.
Step-by-step explanation:
To find the coordinates of the vertex of the quadratic function f(x) = x² - 12x + 5, we can use the vertex formula for a parabola, which is h = -b/(2a) and k = f(h), where h and k are the x and y coordinates of the vertex, respectively, and a and b are coefficients from the quadratic equation in the form ax² + bx + c. In our case, a = 1 and b = -12. Substituting these values into the vertex formula gives us h = -(-12)/(2×1) = 6. To find k, we substitute x = 6 back into the function: k = f(6) = 6² - 12×6 + 5 = 36 - 72 + 5 = -31. Therefore, the vertex is at (6, -31)