Final answer:
The vertex of the quadratic equation y = x² - 6x - 1 is (3, -10), found by using the vertex formula and substituting the calculated h-value back into the original equation.
Step-by-step explanation:
To find the vertex of the quadratic equation y = x² - 6x - 1, we can use the vertex formula which is (h, k) where h is -b/2a and k is the value of the function at h. For the given equation, a equals 1 and b equals -6. Plugging these values into the formula gives us h = -(-6)/2(1) = 3. Substituting x with 3 in the original equation to find k: k = (3)² - 6(3) - 1 = 9 - 18 - 1 = -10. Therefore, the vertex of the quadratic equation is (3, -10).