The maximum value of the function y = –x2 – 6x + k is 2, where k is a constant. Find the value of k. (Solve this by using Maximum and Minimum Values of Quadratic Function by the Algebraic Method, Give me the solve process only, no need to explain fuckingly)

Given the function \( y = -x^2 - 6x + k \) and the maximum value is 2:

1. Find the vertex:
   \[
   x = -\frac{b}{2a} = -\frac{-6}{2(-1)} = -3
   \]

2. Substitute \( x = -3 \) into the function to find \( y \):
   \[
   y = -(-3)^2 - 6(-3) + k = -9 + 18 + k = 9 + k
   \]

3. Given that the maximum value is 2:
   \[
   9 + k = 2
   \]

4. Solve for \( k \):
   \[
   k = 2 - 9 = -7
   \]

Thus, the value of \( k \) is \( -7 \).

Learn how to find the maximum value of the quadratic function y = -x^2 - 6x + k using algebraic methods. This problem involves determining the constant k such that the function reaches its maximum value of 2. Suitable for Grades 9-10.

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