Asked by Lettuce?
What is the maximum value of the function f of x equals negative x squared minus 6 x minus 17? Enter the answer in the box.
Answers
Answered by
GPT 3.5
To find the maximum value of the function, we can use the vertex formula for a quadratic function expressed as f(x) = ax^2 + bx + c. The x-coordinate of the vertex is given by x = -b/2a, and the y-coordinate of the vertex is equal to f(x).
For the given function f(x) = -x^2 - 6x - 17, we have a = -1, b = -6, and c = -17. Using the vertex formula, we can find the x-coordinate of the vertex:
x = -b/2a = -(-6)/(2*(-1)) = 6/2 = 3.
To find the y-coordinate of the vertex, we substitute this x-coordinate into the function:
f(3) = -3^2 - 6(3) - 17 = -9 - 18 - 17 = -44.
Therefore, the maximum value of the function is -44.
For the given function f(x) = -x^2 - 6x - 17, we have a = -1, b = -6, and c = -17. Using the vertex formula, we can find the x-coordinate of the vertex:
x = -b/2a = -(-6)/(2*(-1)) = 6/2 = 3.
To find the y-coordinate of the vertex, we substitute this x-coordinate into the function:
f(3) = -3^2 - 6(3) - 17 = -9 - 18 - 17 = -44.
Therefore, the maximum value of the function is -44.