Question

This problem is solved entirely by hand calculations. Using the first three pairs of data points above, fit the data to a quadratic polynomial of the form f(x)=a₀​+a₁x+a₂​x² Formulate the matrix for the 3×3 system of equations and solve for a₀​,a₁,a₂​ using Gauss elimination by hand. Check that your results are correct by verifying f(2) using your quadratic polynomial coefficients.

Answer 1

The problem requires fitting data to a quadratic polynomial and finding the constants using Gauss elimination, then verifying the results by evaluating the polynomial at x = 2.

Step-by-step explanation:

The student's question involves fitting three data points to a quadratic polynomial of the form f(x) = a₀ + a₁x + a₂x² and solving for the coefficients using Gauss elimination. To create the system of equations, each data point (x, y) results in an equation when plugged into the polynomial form. These equations can be represented as a matrix and solved using Gauss elimination method.

Once the coefficients are found, the verification process involves substituting x = 2 into the polynomial and checking if the obtained result matches the given value for f(2). Solving these quadratic equations requires understanding of basic algebra and systems of equations. Note that graphical methods can be used to estimate the coefficients, but precise calculation needs solving the system.