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Chapter 7: Problem 46

Describe the shape of a scatter plot that suggests modeling the data with a quadratic function.

Short Answer

Expert verified
When a scatter plot shows data that appears to form the shape of a parabola, suggesting a peak or a trough with symmetrical scatter either side of this point, it implies that it may be suitable to model the data using a quadratic function.

Step by step solution

01

Understanding a Quadratic Function

Recognize that a quadratic function is a second-degree polynomial, the graph of which is a parabola. The parabola could either open upwards (if the leading coefficient of the quadratic function is positive) or downwards (if the leading coefficient is negative).
02

Recognize the Shape of Quadratic Function in a Scatter Plot

Scatter plots show the relationship between two sets of data. It would suggest modeling with a quadratic function if the plotted points appear to form the shape of a parabola, i.e., they distribute in such a way that has a evident peak (maximum point for a negative quadratic function) or trough (minimum point for a positive quadratic function), with symmetrical patterns on both sides of the peak or trough.
03

Other Considerations

While determining if a scatter plot suggests a quadratic relationship, the line of best fit can be drawn to help visualize the trend. If this line convincingly forms a parabola, it reinforces that a quadratic model might be suitable.

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