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

Solution:

Given, f(x) = -x² + 6x - 11

We have to find the vertex of the function.

To find the vertex of the function, we have to convert the given function in the form

f(x) = a(x - h)² + k ------------------ (1)

Where, (h, k) is the vertex.

Here, f(x) = -(x² - 6x) - 11

f(x) = -(x² - 2 × 3 × x + 3² -3²) - 11

f(x) = -(x - 3)² + 9 - 11

f(x) = -(x - 3)² - 2 --------------- (2)

Comparing (1) and (2),

h = 3

k = -2

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

Therefore, the coordinates of the vertex is (3, -2).

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

Summary:

The coordinates of the vertex of the graph of the function. f(x) = -x² + 6x - 11 is (3, -2).