Multiple choice

Directions: In the following item, Quantity I and Quantity II are given. Determine the relationship between the quantities and choose the appropriate option. Consider the following curves on the coordinate plane: Curve A: x = 3y2 - 2 and Curve B: x = -2y2 + 5. Quantity I: The x-coordinate of the point where Curve A has its minimum value Quantity II: The x-coordinate of the point where Curve B has its maximum value

  1. Quantity II > Quantity I

  2. Quantity I > Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity II ≥ Quantity I

  5. Quantity I = quantity II, or No relation
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A Correct answer
Explanation

Curve A: x = 3y^2 - 2. The minimum x occurs at y = 0, so x = -2. Curve B: x = -2y^2 + 5. The maximum x occurs at y = 0, so x = 5. Quantity I = -2, Quantity II = 5. Thus, Quantity II > Quantity I.

AI explanation

Curve A, x = 3y^2 - 2, represents a rightward opening parabola, and its minimum x-value occurs at the vertex where y = 0, giving Quantity I as x = -2. Curve B, x = -2y^2 + 5, represents a leftward opening parabola, and its maximum x-value occurs at the vertex where y = 0, giving Quantity II as x = 5. Comparing these vertex coordinates, 5 is greater than -2. Therefore, Quantity II > Quantity I.

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