Calculate the value of [tex]h(-5)[/tex].

Note: Ensure that all steps are shown clearly.

---

Please complete 4 problems.

- Skip
- Check



Answer :

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].