s Use Lagrange interpolation to determine the quadratic polynomial passing through the 3 points: (x0, y0) = (1, 0), (x1, y1) = (2, 11), (x2, y2) = (4, 117).

Question

Use Lagrange interpolation to determine the quadratic polynomial passing through the 3 points: (x0, y0) = (1, 0), (x1, y1) = (2, 11), (x2, y2) = (4, 117).

Answer 1

(1,0), (2,11). (4,117)

quadratic usually means a parabola, but could mean other conic sections, ellipses, circles, hyperbolas

if you restrict it to parabolas, there's still more than one possibility, even if just the standard vertical or horizontal.

but start with upward opening parabola, a quadratic function of the form y = a(x-h)^2 +k

plug in the 3 points and get 3 equations in 3 unknowns, h,k and a.

solve by substitution, elimination or matrix algebra

plot the points, draw a smooth parabolic curve through them. It looks like an upward opening parabola with a>0 or it could be a leftward opening horizontal parabola of general form x=a(y-k)^2 +h

either way, plug in the 3 points, get 3 equations, solve the system for a, h and k