What are the coordinates of the vertex of the graph for the function y = x² + 6x + 11?

To find the coordinates of the vertex of the quadratic function given by y = x² + 6x + 11, we can use the vertex formula. The vertex of a parabola described by the equation y = ax² + bx + c can be found at the point (h, k), where:

• h = -b / (2a)
• k = f(h) (the value of the function at h)

In this case:

• a = 1
• b = 6
• c = 11

First, we will calculate the value of h:

h = -b / (2a) 
  = -6 / (2 * 1) 
  = -6 / 2 
  = -3

Now, we substitute h back into the original equation to find k:

k = f(h) 
  = f(-3) 
  = (-3)² + 6 * (-3) + 11 
  = 9 - 18 + 11 
  = 2

Thus, the vertex of the parabola is at the point:

(h, k) = (-3, 2)

This means that the coordinates of the vertex of the graph of the function y = x² + 6x + 11 are (-3, 2).