Determine the first and second differences for the quadratic pattern.

Step 1: Determine the first and second differences for the quadratic pattern.
The given quadratic pattern is $19; 8; -1; -8; \dots$
First differences:
$D_1 = 8 - 19 = -11$
$D_2 = -1 - 8 = -9$
$D_3 = -8 - (-1) = -7$
Second differences:
$S_1 = -9 - (-11) = 2$
$S_2 = -7 - (-9) = 2$
The second difference is constant and equal to 2.

2.1.1 Determine the next term of the pattern.
The next first difference, $D_4$, is $D_3 + 2 = -7 + 2 = -5$.
The next term, $T_5$, is $T_4 + D_4 = -8 + (-5) = -13$.
The next term is $\boxed{\mathbf{-13}}$.

2.1.2 Determine the general term of the quadratic number pattern.
The general term for a quadratic pattern is $T_n = an^2 + bn + c$.
Using the relationships:
$2a = \text{second difference} \implies 2a = 2 \implies a = 1$.
$3a + b = \text{first term of first differences} \implies 3(1) + b = -11 \implies 3 + b = -11 \implies b = -14$.
$a + b + c = \text{first term of