Exercise 6.7.3

(a)

Find the second degree polynomial $p(x)=q_0+q_{1}x+q_2{x}^2$ that interpolates the three points $(-1,1),(0,0)$, and $(1,1)$ on the graph of $g(x)=|x|$. Sketch $g(x)$ and $p(x)$ over $[-1,1]$ on the same set of axes.

(b)

Find the fourth degree polynomial that interpolates $g(x)=|x|$ at the points $x=-1,-1∕2,0,1∕2$, and 1 . Add a sketch of this polynomial to the graph from (a).