To evaluate [tex]\( h(-1) \)[/tex] for the function [tex]\( h(x) = 3x^2 - 4x + 1 \)[/tex], follow these steps:
1. Substitute [tex]\(-1\)[/tex] for [tex]\(x\)[/tex] in the expression [tex]\( h(x) \)[/tex]:
[tex]\[
h(-1) = 3(-1)^2 - 4(-1) + 1
\][/tex]
2. Evaluate [tex]\((-1)^2\)[/tex]:
[tex]\[
(-1)^2 = 1
\][/tex]
So the expression becomes:
[tex]\[
h(-1) = 3(1) - 4(-1) + 1
\][/tex]
3. Multiply the constants:
[tex]\[
3(1) = 3
\][/tex]
The expression now is:
[tex]\[
h(-1) = 3 - 4(-1) + 1
\][/tex]
4. Multiply [tex]\(-4\)[/tex] by [tex]\(-1\)[/tex]:
[tex]\[
-4(-1) = 4
\][/tex]
Now the expression simplifies to:
[tex]\[
h(-1) = 3 + 4 + 1
\][/tex]
5. Add the constants together:
[tex]\[
3 + 4 + 1 = 8
\][/tex]
Therefore, the value of [tex]\( h(-1) \)[/tex] is:
[tex]\[
h(-1) = 8
\][/tex]
