Question 6
Let $P(x)$ be a quadratic polynomial with real coefficients satisfying $$
\begin{aligned} x^2 - 2x + 2 &\le P(x) \\ &\le 2x^2 - 4x + 3 \end{aligned}
$$ for all real numbers $x,$ and suppose $P(11) = 181.$ Find $P(16).$
\begin{aligned} x^2 - 2x + 2 &\le P(x) \\ &\le 2x^2 - 4x + 3 \end{aligned}
$$ for all real numbers $x,$ and suppose $P(11) = 181.$ Find $P(16).$