Let's analyze the function [tex]\( f(x) = -x^2 + 4x - 2 \)[/tex].
To better understand this function, let's evaluate it at a few specific points.
Step-by-Step Evaluation:
1. Evaluate [tex]\( f(0) \)[/tex]:
[tex]\[
f(0) = -0^2 + 4 \cdot 0 - 2 = 0 + 0 - 2 = -2
\][/tex]
So, [tex]\( f(0) = -2 \)[/tex].
2. Evaluate [tex]\( f(1) \)[/tex]:
[tex]\[
f(1) = -1^2 + 4 \cdot 1 - 2 = -1 + 4 - 2 = 1
\][/tex]
So, [tex]\( f(1) = 1 \)[/tex].
3. Evaluate [tex]\( f(2) \)[/tex]:
[tex]\[
f(2) = -2^2 + 4 \cdot 2 - 2 = -4 + 8 - 2 = 2
\][/tex]
So, [tex]\( f(2) = 2 \)[/tex].
4. Evaluate [tex]\( f(3) \)[/tex]:
[tex]\[
f(3) = -3^2 + 4 \cdot 3 - 2 = -9 + 12 - 2 = 1
\][/tex]
So, [tex]\( f(3) = 1 \)[/tex].
To summarize, we have evaluated the function at four different points:
- [tex]\( f(0) = -2 \)[/tex]
- [tex]\( f(1) = 1 \)[/tex]
- [tex]\( f(2) = 2 \)[/tex]
- [tex]\( f(3) = 1 \)[/tex]
By following these steps, we have found the values of the function [tex]\( f(x) \)[/tex] at the specified points, which are [tex]\((-2, 1, 2, 1)\)[/tex].
