To find [tex]\(h(-8)\)[/tex] for the function [tex]\(h(t) = -2(t + 5)^2 + 4\)[/tex], we need to follow these steps:
1. Substitute [tex]\(t = -8\)[/tex] into the function:
[tex]\[
h(-8) = -2(-8 + 5)^2 + 4
\][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[
-8 + 5 = -3
\][/tex]
3. Square the result of the simplified expression:
[tex]\[
(-3)^2 = 9
\][/tex]
4. Multiply the squared result by [tex]\(-2\)[/tex]:
[tex]\[
-2 \times 9 = -18
\][/tex]
5. Add 4 to the product:
[tex]\[
-18 + 4 = -14
\][/tex]
Therefore, the value of [tex]\(h(-8)\)[/tex] is:
[tex]\[
-14
\][/tex]
The correct answer is [tex]\(-14\)[/tex].
