To solve for [tex]\( h(-8) \)[/tex] given the function [tex]\( h(t) = -2(t + 5)^2 + 4 \)[/tex], follow these steps:
1. Substitute the value [tex]\( t = -8 \)[/tex] into the function:
[tex]\[ h(-8) = -2((-8) + 5)^2 + 4 \][/tex]
2. Simplify the expression inside the parenthesis:
[tex]\[ -8 + 5 = -3 \][/tex]
3. Square the result:
[tex]\[ (-3)^2 = 9 \][/tex]
4. Multiply by -2:
[tex]\[ -2 \times 9 = -18 \][/tex]
5. Add 4 to the result:
[tex]\[ -18 + 4 = -14 \][/tex]
Thus, the value of [tex]\( h(-8) \)[/tex] is [tex]\(-14\)[/tex].
So the correct answer is:
[tex]\[ \boxed{-14} \][/tex]
