What are the coordinates of the vertex of the graph of the function y = –x² + 6x –11?
To find the coordinates of the vertex of the graph of the function y = -x^2 + 6x - 11, we first need to find the x-coordinate of the vertex.
The x-coordinate of the vertex of a quadratic function in the form y = ax^2 + bx + c is given by x = -b/2a. In this case, a = -1 and b = 6.
x = -6 / (2*(-1)) = -6/(-2) = 3
Now, to find the y-coordinate of the vertex, we substitute the x-coordinate (3) into the function:
y = -3^2 + 6(3) - 11 = -9 + 18 - 11 = -2
Therefore, the coordinates of the vertex of the graph of the function y = –x² + 6x –11 are (3, -2).