To find [tex]\( f(-2) \)[/tex] for the function [tex]\( f(x) = 3x^2 - 2x + 7 \)[/tex], follow these steps:
1. Substitute [tex]\(-2\)[/tex] into the function: We need to find [tex]\( f(-2) \)[/tex].
2. Plug in the value: Replace every [tex]\( x \)[/tex] in the function with [tex]\(-2\)[/tex]:
[tex]\[
f(-2) = 3(-2)^2 - 2(-2) + 7
\][/tex]
3. Evaluate the powers and products:
- Calculate [tex]\((-2)^2\)[/tex]:
[tex]\[
(-2)^2 = 4
\][/tex]
- Multiply this result by 3:
[tex]\[
3 \times 4 = 12
\][/tex]
- Calculate [tex]\(-2 \times -2\)[/tex]:
[tex]\[
-2 \times -2 = 4
\][/tex]
4. Add these results together:
- Incorporate the constant 7:
[tex]\[
f(-2) = 12 + 4 + 7
\][/tex]
5. Sum the values:
[tex]\[
12 + 4 + 7 = 23
\][/tex]
Therefore, the value of [tex]\( f(-2) \)[/tex] is [tex]\( 23 \)[/tex]. Thus, the correct answer is [tex]\( 23 \)[/tex].
