Final answer:
The equation h(x)=0.012x² - 0.583x + 35.721 models data within a certain range, and using it outside that range, like the year 1970, yields an incorrect extrapolation. Graphs are essential for comprehending large datasets quickly.
Step-by-step explanation:
The student's question involves using a quadratic regression equation, h(x)=0.012x² - 0.583x + 35.721, to model data between 1940 and 1980. Data points such as h(1985) = 25.52 and h(1990) = 34.275 suggest the projection of some trend, likely related to a certain phenomenon over time. However, the result y = -725 for the year 1970 is nonsensical because it is outside the given range of x values (1981 to 2002), and the calculation was done through extrapolation, which is not reliable with this equation. Additionally, the negative result does not fit the context of the question, which likely relates to counting occurrences, such as flu cases diagnosed where negative numbers are meaningless. Graphical representation of data is emphasized as a valuable tool to compress lots of data and intuitively understand large data points (nearly 600 data points) rather than reading them in numerical form.