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Use quadratic regression to find a function that fits the following points: (1,4) (2,2) (5,8).

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Final answer:

Quadratic regression is used to find a best-fit quadratic function for a set of points by entering the data into a calculator, using its regression function, and adding the resulting equation to a scatter plot.

Step-by-step explanation:

To find a quadratic function that best fits the given points (1,4), (2,2), and (5,8), we need to use quadratic regression. Here's how we can do it:

  • Firstly, enter the data into a calculator's scatter plot function to visualize the distribution of points.
  • Next, use the calculator's regression function to calculate the best-fit quadratic equation. This is typically found under the 'stat' or 'regression' menu on a calculator.
  • The calculator will output a quadratic equation in the form y = ax² + bx + c, where a, b, and c are coefficients that the calculator has determined to minimize the distance of each point from the curve (least-squares method).
  • Finally, add this equation to your scatter plot to visualize the best-fit line.

Rounding the coefficients to four decimal places will give us the most accurate equation that we can use for predictions or analysis.

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