The given quadratic sequence is: $-4, -8, -10, -10, -8$ We need to find an expression for the $n$-th term, $T_n$, of the sequence. Since it's a quadratic sequence, we know the formula will be of the form: $T_n = an^2 + bn + c$

Step 1: First and second differences

Start by calculating the first and second differences.

1st differences: $-8 - (-4) = -4, \quad -10 - (-8) = -2, \quad -10 - (-10) = 0, \quad -8 - (-10) = 2$ So, the first differences are: $-4, -2, 0, 2$.

2nd differences: $-2 - (-4) = 2, \quad 0 - (-2) = 2, \quad 2 - 0 = 2$