To solve for [tex]\( h(-5) \)[/tex] given the function [tex]\( h(x) \)[/tex], follow these steps:
1. Identify the Function:
We're given a function [tex]\( h \)[/tex] which can be defined as:
[tex]\[
h(x) = x^2 + 3x + 2
\][/tex]
2. Substitute the Value:
Substitute [tex]\( x = -5 \)[/tex] into the function.
[tex]\[
h(-5) = (-5)^2 + 3(-5) + 2
\][/tex]
3. Calculate Each Term:
- First, calculate [tex]\( (-5)^2 \)[/tex]:
[tex]\[
(-5)^2 = 25
\][/tex]
- Next, calculate [tex]\( 3(-5) \)[/tex]:
[tex]\[
3(-5) = -15
\][/tex]
- The constant term remains the same:
[tex]\[
2 = 2
\][/tex]
4. Combine All Parts:
Add the results from each term together:
[tex]\[
25 + (-15) + 2 = 25 - 15 + 2
\][/tex]
5. Simplify the Expression:
- First perform the subtraction:
[tex]\[
25 - 15 = 10
\][/tex]
- Then add the remaining term:
[tex]\[
10 + 2 = 12
\][/tex]
So, the value of [tex]\( h(-5) \)[/tex] is [tex]\(\boxed{12}\)[/tex].
