Final answer:
To perform a quadratic regression and find the best fitting quadratic equation for the given points, technology such as a calculator or software is typically used. Assuming a typo in the provided data and ignoring the value '238', quadratic regression would yield coefficients a, b, and c after plotting the points and analyzing the sum of squares of the residuals.
Step-by-step explanation:
To find the equation of a quadratic function that fits the given points using quadratic regression, we first note that a quadratic function has the form f(x) = ax² + bx + c. However, the question appears to have a typo, since it provides five y-values for only four x-values (0, 1, 2, 3). Assuming this is a mistake and disregarding the value '238', we can use the remaining y-values (2, 9, 4, 26) corresponding to the x-values. Applying a quadratic regression analysis, which typically requires the use of a calculator or software, gives us coefficients a, b, and c for the quadratic equation.
To apply this practically, you could arrange the given points in a mathematical software tool that supports regression analysis. Once the points are plotted, the software will calculate the best fitting quadratic equation. If doing this by hand, you would set up a system of equations with the given points, and then solve for 'a', 'b', and 'c'. However, manual calculation can be very cumbersome and is prone to errors, so using technology is recommended for these types of problems.
Without the correct data and technological means to perform the regression, we cannot provide the exact equation here. Still, the general process would involve identifying the coefficients that minimize the sum of the squares of the residuals (the differences between the observed and predicted y-values).