$(7)$ Interpolating data is given as $(t_i,y_i)=\{[(-2,-27)],[(0,-1)],[(1,0)]\}$ Determine the interpolating

by using Lagrage basis. by using Lagrage bass.

$f(t)=y_1{l}_1(t)y_2{l}_2(t)y_3{l}_3(t)$

$f(t)=(-27)\frac{(t-0)(t-1)}{(-2-0)(-2-1)}(-1)\frac{(t-(-2))(t-1)}{(0-(-2))(0-1)}$

$(0)\frac{(t-(-2))(t-0)}{(1-(-2))(1-0)},f(t)=-27\frac{(t-t_2)(t{t}_1)}{(t_1-t_2)(t_1-t_3)}$

$f(t)=-27\frac{t(t-1)}{6}\frac{(t2)(t-1)}{2}=-15t-4t_2$