For the data points in the graphs below, which most likely suggests a quadratic relationship?

• A.
• B.
• C.
• D.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the types of relationships shown in scatter plots. A quadratic relationship typically forms a curved pattern, often resembling a parabola, which can open upwards or downwards.
2. Step 2: Examine the first scatter plot. The points appear scattered without any clear pattern, indicating no obvious relationship between x and y.
3. Step 3: Look at the second scatter plot. The points form a curve that starts low and rises sharply, suggesting a possible quadratic relationship where y increases as x increases, but not linearly.
4. Step 4: Analyze the third scatter plot. The points form a symmetric U-shaped curve, which is a classic sign of a quadratic relationship, as the values decrease and then increase, or vice versa.
5. Step 5: Review the fourth scatter plot. The points show a straight downward trend, indicating a linear negative relationship rather than a quadratic one.