The function f(x) = (x-2)^2 + 5 has its minimum value when x equals?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

The function f(x) = (x-2)^2 + 5 has its minimum value when x equals?

Explanation:
Think about where a parabola reaches its lowest point. This function is a squared term plus a constant, so its minimum occurs when the squared part is zero. That happens when x − 2 = 0, i.e., x = 2. At that point, f(2) = 0 + 5 = 5, which is the smallest value. Any other x makes the square positive, so the function value is larger (for example, x = 0 gives 9, x = 5 gives 14).

Think about where a parabola reaches its lowest point. This function is a squared term plus a constant, so its minimum occurs when the squared part is zero. That happens when x − 2 = 0, i.e., x = 2. At that point, f(2) = 0 + 5 = 5, which is the smallest value. Any other x makes the square positive, so the function value is larger (for example, x = 0 gives 9, x = 5 gives 14).

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