Q. 2) Which type of function best models this data?\begin{tabular}{|c|c|}\hlinex & Y \\\hline−2 & 2.4 \\\hline−1 & 0.2 \\\hline 0 & 0 \\\hline 1 & 1 \\\hline 2 & 5 \\\hline 3 & 10 \\\hline 4 & 17 \\\hline\end{tabular}
Analyze Data Points: Step 1: Analyze the data points to see if they fit a linear, quadratic, or other type of function.Data Points: (−2,2.4),(−1,0.2),(0,0),(1,1),(2,5),(3,10),(4,17)Check for a linear pattern by calculating the differences between consecutive y-values.Differences: 0.2−2.4=−2.2, 0−0.2=−0.2, 1−0=1, 5−1=4, 10−5=5, 17−10=7Since differences are not constant, it's not linear.
Check for Quadratic Pattern: Step 2: Check for a quadratic pattern by calculating the differences of the differences (second differences).Second Differences: −2.2−(−0.2)=−2, 1−(−0.2)=1.2, 4−1=3, 5−4=1, 7−5=2Since second differences are not constant, it's not a perfect quadratic but it seems to be closer to quadratic than linear.
Plot Points for Best Fit: Step 3: Plot the points to visually determine the best fit.Plotting points on a graph, the shape of the curve appears to be more parabolic, suggesting a quadratic function might be a better fit despite the imperfect second differences.
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