To find the coordinates of the vertex of the quadratic function y = x² + 6x + 11, we can use the vertex formula. A quadratic equation in the standard form y = ax² + bx + c has its vertex at the point (h, k), where:
- h = -b / (2a)
- k = f(h) (where f(h) is the function evaluated at h)
In our case, a = 1, b = 6, and c = 11.
Now, we can calculate h:
h = -6 / (2 * 1) = -6 / 2 = -3
Next, we need to find k by substituting -3 back into the function:
k = f(-3) = (-3)² + 6(-3) + 11
k = 9 – 18 + 11 = 2
Thus, the vertex coordinates are (-3, 2).
In conclusion, the coordinates of the vertex of the graph of the function y = x² + 6x + 11 are (-3, 2).