Quadratic trend requires:

Quadratic trend requires:

• A. At least three ordered conditions and one change in direction leading to a U-shaped curve.
• B. At least two ordered conditions with a linear trend.
• C. Four or more conditions with multiple direction changes.
• D. No conditions, only two variables.

Answer: (A)

A quadratic trend captures curvature in how a variable changes over time by including a squared time term. To estimate that curvature you need enough time points to observe a bend in the trajectory, which requires at least three ordered observations. With three or more points, the trend can bend once, producing a U-shaped (or inverted U-shaped) pattern depending on the sign of the quadratic term. In short, you need three ordered conditions to detect curvature, and a single change in direction signals that nonlinearity. The other descriptions don’t fit because two points can only show a straight line (linear trend), and more points or multiple direction changes imply more complex patterns than the simple quadratic.

A quadratic trend captures curvature in how a variable changes over time by including a squared time term. To estimate that curvature you need enough time points to observe a bend in the trajectory, which requires at least three ordered observations. With three or more points, the trend can bend once, producing a U-shaped (or inverted U-shaped) pattern depending on the sign of the quadratic term. In short, you need three ordered conditions to detect curvature, and a single change in direction signals that nonlinearity.

The other descriptions don’t fit because two points can only show a straight line (linear trend), and more points or multiple direction changes imply more complex patterns than the simple quadratic.