<p>(a) \(y = 1 - x^2, x \in [-1, 1], y \in [-1, 0]\)</p>
<p>(b) \(y = 1 - x^2, x \in [-2, 2], y \in [0, 1]\)</p>
<p>(c) \(y = 1 - x^2, x \in [-2, 2], y \in [-3, 1]\)</p>
<p>(d) \(y = 1 - x^2, x \in [-1, 1], y \in [0, 1]\)</p>
Step-by-Step Solution
Key Concept: Determine the locus by identifying the constraints on the parabola's vertex position.
<p><strong>Solution:</strong> The locus of the vertex satisfies \(y = 1 - x^2\) with the domain and range constraints \(x \in [-1, 1], y \in [0, 1]\).</p>
Correct Answer: D