Question

What are the coordinates of the vertex of the graph of the function y = –x² + 6x –11? (1 point) Responses (3, –2) (3, –2) (3, 16) (3, 16) (–3, –29) (–3, –29) (–3, –20)

Answer 1

To find the coordinates of the vertex of the graph of the function y = –x² + 6x –11, we first need to rewrite the equation in vertex form.

The vertex form of a quadratic function is y = a(x - h)² + k, where (h, k) are the coordinates of the vertex.

Using the given function y = –x² + 6x – 11, we can rewrite it as:

y = -(x² - 6x + 9) - 11 + 9 // Completing the square by adding and subtracting (6/2)² = 9 inside the parenthesis
y = -(x - 3)² - 2 // Simplifying

Now we can see that the vertex of the graph is (3, -2).

Answer: (3, -2)