What are the coordinates of the vertex of the graph of the function y = -x^2 + 6x - 11?
To find the coordinates of the vertex of the graph of the function y = -x^2 + 6x - 11, we first need to rewrite the function in the form y = a(x - h)^2 + k, where (h,k) are the coordinates of the vertex.
Starting with the given function y = -x^2 + 6x - 11, we complete the square to rewrite it in the vertex form:
y = -(x^2 - 6x + 9) - 11 + 9
y = -(x - 3)^2 - 2
Therefore, the vertex of the graph of the function y = -x^2 + 6x - 11 is at (3, -2).