The paper “Effects of Age and Gender on Physical Performance” (Age [2007]: 77–85) describes a study of the relationship between age and 1-hour swimming performance. Data on age and swim distance for over 10,000 men participating in a national long-distance 1-hour swimming competition are summarized in the accompanying table. In Exercise 5.34 from Section 5.3, a plot of the residuals from the least-squares line showed a curved pattern that suggested that a quadratic curve would do a better job of summarizing the relationship between x representative age and y average swim distance. Find the equation of the least-squares quadratic curve and use it to predict average swim distance at 40 years of age.

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Average Swim Age Representative Age Distance Group (Midpoint of Age Group) (meters) 20-29 25 3913.5 30-39 35 3728.8 40-49 45 3579.4 50-59 55 3361.9 60-69 65 3000.1 70-79 75 2649.0 80-89 85 2118.4