To find the vertex of the quadratic function [tex]\( y = x^2 - 2x + 1 \)[/tex], follow these steps:
1. Identify the coefficients: The given quadratic function is in the form [tex]\( y = ax^2 + bx + c \)[/tex], where [tex]\( a = 1 \)[/tex], [tex]\( b = -2 \)[/tex], and [tex]\( c = 1 \)[/tex].
2. Find the x-coordinate of the vertex: The x-coordinate of the vertex for a quadratic function is found using the formula [tex]\( x = -\frac{b}{2a} \)[/tex].
Substituting the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
[tex]\[
x = -\frac{-2}{2 \cdot 1} = \frac{2}{2} = 1
\][/tex]
3. Find the y-coordinate of the vertex: Once we have the x-coordinate, we substitute it back into the original function to find the corresponding y-coordinate.
Substituting [tex]\( x = 1 \)[/tex] into the function [tex]\( y = x^2 - 2x + 1 \)[/tex]:
[tex]\[
y = (1)^2 - 2(1) + 1 = 1 - 2 + 1 = 0
\][/tex]
4. Write the vertex: The vertex of the function is the point [tex]\((x, y)\)[/tex].
Therefore, the vertex of the function [tex]\( y = x^2 - 2x + 1 \)[/tex] is [tex]\((1, 0)\)[/tex].
Hence, the correct answer is:
B. [tex]\((1, 0)\)[/tex]
