Sure, let’s find [tex]\( h(-8) \)[/tex] given the function [tex]\( h(t) = -2(t + 5)^2 + 4 \)[/tex].
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]\[
-8 + 5 = -3
\][/tex]
So the expression becomes:
[tex]\[
h(-8) = -2(-3)^2 + 4
\][/tex]
3. Square the value inside the parentheses:
[tex]\[
(-3)^2 = 9
\][/tex]
So the expression now is:
[tex]\[
h(-8) = -2 \cdot 9 + 4
\][/tex]
4. Multiply the squared value by [tex]\(-2\)[/tex]:
[tex]\[
-2 \cdot 9 = -18
\][/tex]
So the expression now is:
[tex]\[
h(-8) = -18 + 4
\][/tex]
5. Add [tex]\( 4 \)[/tex] to [tex]\(-18\)[/tex]:
[tex]\[
-18 + 4 = -14
\][/tex]
Thus, the value of [tex]\( h(-8) \)[/tex] is [tex]\(\boxed{-14}\)[/tex].
