Problem

If , what is the minimum value of for real numbers ?

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Step-by-Step Solution

🟦 Step 1: Recognize the function type

This is a quadratic function:

It opens upward (since ), so it has a minimum at the vertex.

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🟦 Step 2: Use the vertex formula

The vertex of a parabola is at:

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🟦 Step 3: Plug in the vertex to find the minimum

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✅ Final Answer:

The minimum value of is:

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📈 Visual Insight (Coming Soon!)

(We’ll later add a parabola plot here that shows the vertex at (2, -1))