To evaluate [tex]\( h(-1) \)[/tex] given the function [tex]\( h(x) = 3x^2 - 4x + 1 \)[/tex], follow these steps:
1. Start by substituting [tex]\(-1\)[/tex] for [tex]\( x \)[/tex] in the function:
[tex]\[
h(-1) = 3(-1)^2 - 4(-1) + 1
\][/tex]
2. Calculate [tex]\((-1)^2\)[/tex]:
[tex]\[
(-1)^2 = 1
\][/tex]
3. Substitute this back into the equation:
[tex]\[
h(-1) = 3 \cdot 1 - 4(-1) + 1
\][/tex]
4. Multiply [tex]\(3\)[/tex] by [tex]\(1\)[/tex]:
[tex]\[
3 \cdot 1 = 3
\][/tex]
5. Next, calculate [tex]\(-4 \cdot (-1)\)[/tex]:
[tex]\[
-4 \cdot (-1) = 4
\][/tex]
6. Substitute these results back into the equation:
[tex]\[
h(-1) = 3 + 4 + 1
\][/tex]
7. Finally, add the terms together:
[tex]\[
h(-1) = 3 + 4 + 1 = 8
\][/tex]
Therefore, the value of [tex]\( h(-1) \)[/tex] is:
[tex]\[
h(-1) = 8
\][/tex]
