To evaluate [tex]\( h(-1) \)[/tex] for the given function [tex]\( h(x) = 3x^2 - 4x + 1 \)[/tex], follow these steps:
1. Substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( h(x) \)[/tex].
[tex]\[
h(-1) = 3(-1)^2 - 4(-1) + 1
\][/tex]
2. Calculate [tex]\( (-1)^2 \)[/tex].
[tex]\[
(-1)^2 = 1
\][/tex]
So the expression becomes:
[tex]\[
h(-1) = 3 \cdot 1 - 4(-1) + 1
\][/tex]
3. Multiply the terms by their coefficients.
[tex]\[
3 \cdot 1 = 3
\][/tex]
[tex]\[
-4 \cdot (-1) = 4
\][/tex]
So the expression now is:
[tex]\[
h(-1) = 3 + 4 + 1
\][/tex]
4. Add the terms together.
[tex]\[
3 + 4 + 1 = 8
\][/tex]
Thus, [tex]\( h(-1) = 8 \)[/tex].
