MathNet 2010 — Part 03 Question 115

Let $p(x)$ be a polynomial of degree $2$ such that $|p(x)| \le 1$ holds for $x \in \{-1, 0, 1\}$. Show that for every $x \in [-1, 1]$
$$
|p(x)| \le \frac{5}{4}
$$