Question

select the correct answer.

which set of data could be reasonably modeled by a quadratic function?

both graphs
graph a
graph b
neither graph

Explanation:

Analyze the shape of Graph A

The data points in Graph A decrease from \(x = 0\) to approximately \(x = 4\), reach a minimum point, and then increase from \(x = 4\) to \(x = 8\), forming a clear U-shaped curve (parabola opening upward).

Analyze the shape of Graph B

The data points in Graph B increase from \(x = 0\) to approximately \(x = 7\), reach a maximum point, and then decrease from \(x = 7\) to \(x = 12\), forming a clear inverted U-shaped curve (parabola opening downward).

Determine the appropriate model

Since both Graph A (upward parabola) and Graph B (downward parabola) exhibit symmetric, single-bend curved patterns characteristic of quadratic functions, both sets of data can be reasonably modeled by a quadratic function.

Answer:

• both graphs (Correct answer)
• graph A
• graph B
• neither graph