---

Solution

$p(x) = ax^2 + bx + c$, $p(0)=1 \Rightarrow c=1$

$p(1) = 4 \Rightarrow a + b = 3 \quad \cdots(1)$
$p(-1) = 6 \Rightarrow a - b = 5 \quad \cdots(2)$

$(1)+(2) \Rightarrow a = 4, \quad (1)-(2) \Rightarrow b = -1$

$\therefore p(x) = 4x^2 - x + 1$

$p(2) = 16 - 2 + 1 = 15 \neq 11 \quad \text{(1)} \times$
$p(2) = 15 \neq 19 \quad \text{(2)} \times$
$p(-2) = 16 + 2 + 1 = 19 \quad \text{(3)} \checkmark$
$p(-2) = 19 \neq 11 \quad \text{(4)} \times$

Answer: Option 3, $p(-2) = 19$