What is the maximum value of f(x) = -x^2 + 6x - 8? (2023)

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Question: What is the maximum value of f(x) = -x^2 + 6x - 8? (2023)

Options:

Correct Answer: 6

Solution:

The vertex occurs at x = 3. f(3) = -9 + 18 - 8 = 1.

What is the maximum value of f(x) = -x^2 + 6x - 8? (2023)

What is the maximum value of f(x) = -x^2 + 6x - 8? (2023)

Step 1: Identify the function we are working with, which is f(x) = -x^2 + 6x - 8.
Step 2: Recognize that this is a quadratic function in the form of f(x) = ax^2 + bx + c, where a = -1, b = 6, and c = -8.
Step 3: Find the x-coordinate of the vertex using the formula x = -b/(2a). Here, b = 6 and a = -1.
Step 4: Calculate x = -6/(2 * -1) = -6/-2 = 3.
Step 5: Now, substitute x = 3 back into the function to find the maximum value: f(3) = -3^2 + 6*3 - 8.
Step 6: Calculate f(3): f(3) = -9 + 18 - 8.
Step 7: Simplify the expression: -9 + 18 = 9, and then 9 - 8 = 1.
Step 8: Therefore, the maximum value of f(x) is 1.

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