Consider the points $\left\{x_{0}=\frac{1}{2}, x_{1}=\frac{3}{4}, x_{2}=\frac{4}{5}\right\}$ in $[0,1] .$ What should $\left\{a_{0}, a_{1}, a_{2}\right\}$ be so that the estimate $\int_{0}^{1} f(x) d x \approx a_{0} \cdot f\left(x_{0}\right)+a_{1} \cdot f\left(x_{1}\right)+a_{2} \cdot f\left(x_{2}\right)$ is exact for $f(x)$ a polynomial of degree $k \leq 2 ?$