What is the minimum value of f(x) = 3x^2 - 12x + 7? (2022)

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Question: What is the minimum value of f(x) = 3x^2 - 12x + 7? (2022)

Options:

Correct Answer: -5

Exam Year: 2022

Solution:

The vertex occurs at x = 2. f(2) = -5.

What is the minimum value of f(x) = 3x^2 - 12x + 7? (2022)

What is the minimum value of f(x) = 3x^2 - 12x + 7? (2022)

Step 1: Identify the function we are working with, which is f(x) = 3x^2 - 12x + 7.
Step 2: Recognize that this is a quadratic function in the form of ax^2 + bx + c, where a = 3, b = -12, and c = 7.
Step 3: Find the x-coordinate of the vertex using the formula x = -b / (2a). Here, b = -12 and a = 3.
Step 4: Calculate x = -(-12) / (2 * 3) = 12 / 6 = 2.
Step 5: Now, substitute x = 2 back into the function to find the minimum value: f(2) = 3(2^2) - 12(2) + 7.
Step 6: Calculate f(2) = 3(4) - 24 + 7 = 12 - 24 + 7 = -5.
Step 7: Therefore, the minimum value of f(x) is -5.

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