Alright, let's evaluate the quadratic function [tex]\( f(x) = 3x^2 - 4x + 2 \)[/tex] for the given inputs [tex]\( x = -4 \)[/tex], [tex]\( x = 0 \)[/tex], and [tex]\( x = 1 \)[/tex].
### Step-by-Step Solution:
#### 1. Evaluate [tex]\( f(-4) \)[/tex]:
Plug [tex]\( x = -4 \)[/tex] into the function:
[tex]\[
f(-4) = 3(-4)^2 - 4(-4) + 2
\][/tex]
Calculate each term separately:
[tex]\[
(-4)^2 = 16
\][/tex]
[tex]\[
3 \times 16 = 48
\][/tex]
[tex]\[
-4 \times -4 = 16
\][/tex]
Add all terms together:
[tex]\[
f(-4) = 48 + 16 + 2 = 66
\][/tex]
So, [tex]\( f(-4) = 66 \)[/tex].
#### 2. Evaluate [tex]\( f(0) \)[/tex]:
Plug [tex]\( x = 0 \)[/tex] into the function:
[tex]\[
f(0) = 3(0)^2 - 4(0) + 2
\][/tex]
Calculate each term separately:
[tex]\[
0^2 = 0
\][/tex]
[tex]\[
3 \times 0 = 0
\][/tex]
[tex]\[
-4 \times 0 = 0
\][/tex]
Add all terms together:
[tex]\[
f(0) = 0 + 0 + 2 = 2
\][/tex]
So, [tex]\( f(0) = 2 \)[/tex].
#### 3. Evaluate [tex]\( f(1) \)[/tex]:
Plug [tex]\( x = 1 \)[/tex] into the function:
[tex]\[
f(1) = 3(1)^2 - 4(1) + 2
\][/tex]
Calculate each term separately:
[tex]\[
1^2 = 1
\][/tex]
[tex]\[
3 \times 1 = 3
\][/tex]
[tex]\[
-4 \times 1 = -4
\][/tex]
Add all terms together:
[tex]\[
f(1) = 3 - 4 + 2 = 1
\][/tex]
So, [tex]\( f(1) = 1 \)[/tex].
### Final Results:
- [tex]\( f(-4) = 66 \)[/tex]
- [tex]\( f(0) = 2 \)[/tex]
- [tex]\( f(1) = 1 \)[/tex]
These evaluations provide the values of the quadratic function at the specified points.
