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The scatterplot shows monthly high temperatures in Austin, Texas, across a 12-month period. The question asks which function best models the data from month 1 to month 9.

From the scatterplot, the temperatures generally rise from month 1 (January) to around month 7 (July or August), peaking, and then slowly decreasing. This shape suggests that a quadratic function or possibly a sinusoidal function might model the data well, given the clear increase followed by a leveling off or slight decrease.

To model the data from month 1 to month 9, a quadratic function of the form \( T(x) = ax^2 + bx + c \) might fit, where \( x \) is the month, and \( T(x) \) is the temperature. The data appears to peak somewhere around month 7 or 8 and then begin decreasing slightly towards month 9.

Would you like more details on how to derive the equation, or perhaps a step-by-step explanation of how to fit a quadratic model?

Here are 5 related questions to expand the topic:

1. How do you determine the best function to model a dataset from a scatterplot?
2. What is the general shape of a quadratic function, and how does it relate to real-world data?
3. Can you explain the differences between linear, quadratic, and sinusoidal models for temperature data?
4. How do you calculate the coefficients of a quadratic function that fits a given dataset?
5. What role do residuals play in determining how well a model fits the data?

**Tip:** When analyzing scatterplots, always consider both the direction and curvature of the data points to identify the type of function that may model them best.

The scatterplot shows the monthly high temperatures for Austin, Texas, across a 12-month period. The question asks which function best models the data from month 1 to month 9.

Learn how to model monthly high temperatures in Austin, Texas, using a quadratic function. The data from month 1 to month 9 suggests a peak in summer, making a quadratic function a good fit. Suitable for students in Grades 9-12.

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