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