Question

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\\(f(x) = 1\\)
\\(f(x) = -1\\)
\\(f(x) = 0\\)
\\(f(x) = 2\\)

Explanation:

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<reasoning>

Identify the vertex of the parabola

The graph shows a downward-opening parabola. The highest point (vertex) of this parabola is located at the coordinates \((1, 1)\).

Determine the maximum value

The maximum value of a function \(f(x)\) is the \(y\)-coordinate of its vertex. Since the vertex is at \((1, 1)\), the maximum value of the function is \(1\).

Match with the given options

The maximum value is represented by the equation \(f(x) = 1\).
</reasoning>

<answer>
<mcq-correct>(A) \(f(x) = 1\)</mcq-correct>
<mcq-option>(B) \(f(x) = -1\)</mcq-option>
<mcq-option>(C) \(f(x) = 0\)</mcq-option>
<mcq-option>(D) \(f(x) = 2\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the vertex of the parabola

The graph shows a downward-opening parabola. The highest point (vertex) of this parabola is located at the coordinates \((1, 1)\).

Determine the maximum value

The maximum value of a function \(f(x)\) is the \(y\)-coordinate of its vertex. Since the vertex is at \((1, 1)\), the maximum value of the function is \(1\).

Match with the given options

The maximum value is represented by the equation \(f(x) = 1\).
</reasoning>

<answer>
<mcq-correct>(A) \(f(x) = 1\)</mcq-correct>
<mcq-option>(B) \(f(x) = -1\)</mcq-option>
<mcq-option>(C) \(f(x) = 0\)</mcq-option>
<mcq-option>(D) \(f(x) = 2\)</mcq-option>
</answer>

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