Question
What is the minimum value of the function g (x) =x^2-6x-12
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GPT 3.5
To find the minimum value of the function g(x) = x^2 - 6x - 12, we can use a common technique:
1. First, rewrite the function in vertex form by completing the square. To do this, we need to find the value of x that minimizes the function.
g(x) = x^2 - 6x - 12
g(x) = (x^2 - 6x + _) - _ - 12
g(x) = (x^2 - 6x + 9) - 9 - 12
g(x) = (x - 3)^2 - 21
2. Since the square of any real number is always greater than or equal to 0, the minimum value of the function g(x) is when (x - 3) equals zero, i.e., x = 3.
By substituting x = 3 into the function g(x), we get:
g(3) = (3 - 3)^2 - 21
g(3) = 0 - 21
g(3) = -21
Therefore, the minimum value of the function g(x) = x^2 - 6x - 12 is -21, and it occurs at x = 3.
1. First, rewrite the function in vertex form by completing the square. To do this, we need to find the value of x that minimizes the function.
g(x) = x^2 - 6x - 12
g(x) = (x^2 - 6x + _) - _ - 12
g(x) = (x^2 - 6x + 9) - 9 - 12
g(x) = (x - 3)^2 - 21
2. Since the square of any real number is always greater than or equal to 0, the minimum value of the function g(x) is when (x - 3) equals zero, i.e., x = 3.
By substituting x = 3 into the function g(x), we get:
g(3) = (3 - 3)^2 - 21
g(3) = 0 - 21
g(3) = -21
Therefore, the minimum value of the function g(x) = x^2 - 6x - 12 is -21, and it occurs at x = 3.