The image shows a scatter plot titled "Stock Price and Time," with data points plotted over time. The x-axis represents "Week," and the y-axis represents "Stock Price (dollars)." The data points form a parabolic shape, where the stock price increases initially, reaches a peak, and then decreases.

The question asks which type of function best models this data. The answer choices are:

A. A quadratic function with a negative value of a
B. A square root function
C. A linear function with a positive slope
D. A quadratic function with a positive value of a

Analysis:

The graph appears to resemble a parabola opening downward. This shape indicates a quadratic function where the coefficient of the squared term (a) is negative.

Correct Answer:

A. A quadratic function with a negative value of a

This is because the graph shows a parabolic curve opening downwards, which matches the characteristics of a quadratic function with a negative leading coefficient.

Would you like more details on how to identify the characteristics of different types of functions from a graph, or do you have any other questions?

Related Questions:

1. How do you determine the direction of a quadratic function from its equation?
2. What are the key differences between linear, quadratic, and square root functions?
3. How does the coefficient "a" affect the shape of a quadratic function?
4. What are real-life applications of modeling data with quadratic functions?
5. How can you use vertex form to determine the maximum or minimum value of a quadratic function?

Tip: When identifying the type of function that fits a graph, observe the overall shape and direction of the curve. Quadratic functions form parabolas, while linear functions create straight lines.