To find [tex]\( h(-8) \)[/tex] for the given function [tex]\( h(t) = -2(t+5)^2 + 4 \)[/tex], follow these steps:
1. Substitute [tex]\( t = -8 \)[/tex] into the function:
[tex]\( h(-8) = -2(-8 + 5)^2 + 4 \)[/tex]
2. Simplify inside the parentheses:
Compute [tex]\( -8 + 5 \)[/tex]:
[tex]\[ -8 + 5 = -3 \][/tex]
3. Square the result of the parentheses:
Compute [tex]\( (-3)^2 \)[/tex]:
[tex]\[ (-3)^2 = 9 \][/tex]
4. Multiply by -2:
Compute [tex]\( -2 \cdot 9 \)[/tex]:
[tex]\[ -2 \cdot 9 = -18 \][/tex]
5. Add 4 to the result:
Compute [tex]\( -18 + 4 \)[/tex]:
[tex]\[ -18 + 4 = -14 \][/tex]
Therefore, [tex]\( h(-8) = -14 \)[/tex].
Thus, the correct answer is:
[tex]\[ -14 \][/tex]
