To find [tex]\( h(-8) \)[/tex] given the function [tex]\( h(t) = -2(t+5)^2 + 4 \)[/tex], we will 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:
[tex]\[
-8 + 5 = -3
\][/tex]
Thus,
[tex]\[
h(-8) = -2(-3)^2 + 4
\][/tex]
3. Square the value inside the parentheses:
[tex]\[
(-3)^2 = 9
\][/tex]
So the equation becomes:
[tex]\[
h(-8) = -2 \cdot 9 + 4
\][/tex]
4. Multiply [tex]\(-2\)[/tex] by [tex]\( 9 \)[/tex]:
[tex]\[
-2 \cdot 9 = -18
\][/tex]
Now the equation is:
[tex]\[
h(-8) = -18 + 4
\][/tex]
5. Add [tex]\( 4 \)[/tex] to [tex]\(-18\)[/tex]:
[tex]\[
-18 + 4 = -14
\][/tex]
Hence, [tex]\( h(-8) = -14 \)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{-14}
\][/tex]
