To find the value of [tex]\( C(-2) \)[/tex] where the function [tex]\( C(t) \)[/tex] is defined as:
[tex]\[ C(t) = t^2 - 2t - 4 \][/tex]
we follow these steps:
1. Substitute [tex]\( t = -2 \)[/tex] into the function [tex]\( C(t) \)[/tex]:
[tex]\[
C(-2) = (-2)^2 - 2(-2) - 4
\][/tex]
2. Compute the square of [tex]\( -2 \)[/tex]:
[tex]\[
(-2)^2 = 4
\][/tex]
3. Compute [tex]\( -2 \times (-2) \)[/tex]:
[tex]\[
-2 \times (-2) = 4
\][/tex]
4. Combine these results:
[tex]\[
C(-2) = 4 + 4 - 4
\][/tex]
5. Simplify the expression by performing the addition and subtraction:
[tex]\[
4 + 4 = 8
\][/tex]
[tex]\[
8 - 4 = 4
\][/tex]
Thus, the value of [tex]\( C(-2) \)[/tex] is:
[tex]\[
\boxed{4}
\][/tex]
