Final answer:
The question involves constructing a quadratic Lagrange Polynomial for given data points. This interpolation process uses Lagrange basis polynomials to determine the coefficients of the polynomial, which are then used to form the final quadratic equation.
Step-by-step explanation:
The student is asking how to construct the quadratic Lagrange Polynomial that interpolates the given data points: (-10,10), (20,58), (1019,-32). A quadratic Lagrange Polynomial is of the form L(x) = a*x2 + b*x + c, where a, b, and c are constants determined by the given data points. The method involves using the Lagrange basis polynomials where each basis polynomial is constructed such that it is 1 at one data point and 0 at the others. The formula for the Lagrange basis polynomials is:
Lk(x) = Πj=0, j≠kn (x - xj) / (xk - xj)
For three points, we construct L0(x), L1(x), and L2(x), and then sum them up after multiplying each by the corresponding y-value of the data point it represents. After calculations, we combine and simplify to get the final form of the quadratic polynomial.