We are given the quadratic equation $y = -2x^2 + 4x + 9$, and we need to complete the table of values by calculating the values for $A$ and $B$.

Step 1: Calculate $A$ when $x = -1$

Substitute $x = -1$ into the equation $y = -2x^2 + 4x + 9$:

$y = -2(-1)^2 + 4(-1) + 9 = -2(1) - 4 + 9 = -2 - 4 + 9 = 3$

So, $A = 3$.

Step 2: Calculate $B$ when $x = 2$

Substitute $x = 2$ into the equation $y = -2x^2 + 4x + 9$:

$y = -2(2)^2 + 4(2) + 9 = -2(4) + 8 + 9 = -8 + 8 + 9 = 9$

So, $B = 9$.

Final Table: