To solve for [tex]\( y \)[/tex] when [tex]\( x = -2 \)[/tex] in the polynomial function [tex]\( y = x^2 - 4x + 4 \)[/tex], we will substitute [tex]\( x = -2 \)[/tex] into the equation and simplify step by step.
1. Start with the given polynomial function:
[tex]\[
y = x^2 - 4x + 4
\][/tex]
2. Substitute [tex]\( x = -2 \)[/tex] into the equation:
[tex]\[
y = (-2)^2 - 4(-2) + 4
\][/tex]
3. Calculate each term separately:
- The first term is [tex]\((-2)^2\)[/tex]:
[tex]\[
(-2)^2 = 4
\][/tex]
- The second term is [tex]\(-4(-2)\)[/tex]:
[tex]\[
-4 \times (-2) = 8
\][/tex]
- The third term is simply [tex]\(4\)[/tex].
4. Combine all the calculated terms:
[tex]\[
y = 4 + 8 + 4
\][/tex]
5. Add the terms together to get the final value of [tex]\( y \)[/tex]:
[tex]\[
y = 16
\][/tex]
So, when [tex]\( x = -2 \)[/tex], the value of [tex]\( y \)[/tex] is:
[tex]\[
y = 16
\][/tex]
