Final answer:
Fitting a parabolic function to data points involves using the method of least squares, which is typically done with a calculator's regression function to find the optimal coefficients for the model. The goal is to minimize the sum of the squares of the residuals between actual data points and the predicted values.
Step-by-step explanation:
The method of least squares is a statistical technique used to find the best-fitting curve to a set of data points by minimizing the sum of the squares of the offsets (residuals) of the points from the curve. To fit a parabolic function y = αx² + βx to the given data points using least squares, follow these steps:
- Enter the data into a calculator and make a scatter plot.
- Use the calculator's regression function to find the coefficients α (alpha) and β (beta) that minimize the squared differences between the observed values and the values predicted by the parabolic model.
- Draw the resulting parabolic curve on the scatter plot to visualize the fit.
The slope and y-intercept of the least-squares line can also be calculated manually using mathematical formulas, but in this case, utilizing a calculator's built-in functions will greatly simplify the process.