Alright, let's evaluate the given function [tex]\( f(x) = 7x^2 - 6x + 1 \)[/tex] at different values of [tex]\( x \)[/tex].
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[
f(-2) = 7(-2)^2 - 6(-2) + 1
\][/tex]
[tex]\[
(-2)^2 = 4
\][/tex]
[tex]\[
7 \cdot 4 = 28
\][/tex]
[tex]\[
-6 \cdot (-2) = 12
\][/tex]
[tex]\[
28 + 12 + 1 = 41
\][/tex]
So, [tex]\( f(-2) = 41 \)[/tex].
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[
f(-1) = 7(-1)^2 - 6(-1) + 1
\][/tex]
[tex]\[
(-1)^2 = 1
\][/tex]
[tex]\[
7 \cdot 1 = 7
\][/tex]
[tex]\[
-6 \cdot (-1) = 6
\][/tex]
[tex]\[
7 + 6 + 1 = 14
\][/tex]
So, [tex]\( f(-1) = 14 \)[/tex].
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = 7(0)^2 - 6(0) + 1
\][/tex]
[tex]\[
0 = 0
\][/tex]
[tex]\[
7 \cdot 0 = 0
\][/tex]
[tex]\[
-6 \cdot 0 = 0
\][/tex]
[tex]\[
0 + 0 + 1 = 1
\][/tex]
So, [tex]\( f(0) = 1 \)[/tex].
4. For [tex]\( x = 1 \)[/tex]:
[tex]\[
f(1) = 7(1)^2 - 6(1) + 1
\][/tex]
[tex]\[
(1)^2 = 1
\][/tex]
[tex]\[
7 \cdot 1 = 7
\][/tex]
[tex]\[
-6 \cdot 1 = -6
\][/tex]
[tex]\[
7 - 6 + 1 = 2
\][/tex]
So, [tex]\( f(1) = 2 \)[/tex].
5. For [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = 7(2)^2 - 6(2) + 1
\][/tex]
[tex]\[
(2)^2 = 4
\][/tex]
[tex]\[
7 \cdot 4 = 28
\][/tex]
[tex]\[
-6 \cdot 2 = -12
\][/tex]
[tex]\[
28 - 12 + 1 = 17
\][/tex]
So, [tex]\( f(2) = 17 \)[/tex].
Thus, the calculated values of the function are:
[tex]\[
f(-2) = 41
\][/tex]
[tex]\[
f(-1) = 14
\][/tex]
[tex]\[
f(0) = 1
\][/tex]
[tex]\[
f(1) = 2
\][/tex]
[tex]\[
f(2) = 17
\][/tex]
