Final answer:
The least square approximation of a function at given points is found by applying the method of least squares to the type ax^2 + bx + c, using the quadratic formula to solve the system of equations for the coefficients.
Step-by-step explanation:
To determine the least square approximation of the type a * x^2 + bx + c to the function 2*, at the points xi = 0, 1, 2, 3, 4, we need to apply the method of least squares. This involves setting up a system of equations derived from the partial derivatives of the sum of squared residuals with respect to the coefficients a, b, and c and solving for these coefficients to find the best fit quadratic approximation.
The general form of a quadratic equation is given by ax^2 + bx + c = 0. The solutions or roots for any quadratic equation can be calculated using the quadratic formula, -b ± √(b^2 - 4ac) / (2a).