To find the vertex of the parabola given by the function [tex]\( y = x^2 - 4x + 3 \)[/tex], we need to use the vertex formula for a quadratic function of the form [tex]\( y = ax^2 + bx + c \)[/tex]. The vertex formula tells us that the x-coordinate of the vertex is given by:
[tex]\[
x_{\text{vertex}} = -\frac{b}{2a}
\][/tex]
Here, [tex]\(a = 1\)[/tex], [tex]\(b = -4\)[/tex], and [tex]\(c = 3\)[/tex].
1. Calculate the x-coordinate of the vertex:
[tex]\[
x_{\text{vertex}} = -\frac{-4}{2 \times 1} = \frac{4}{2} = 2
\][/tex]
2. Substitute [tex]\( x_{\text{vertex}} = 2 \)[/tex] back into the original equation to find the y-coordinate:
[tex]\[
y = (2)^2 - 4(2) + 3
\][/tex]
[tex]\[
y = 4 - 8 + 3
\][/tex]
[tex]\[
y = -1
\][/tex]
So, the vertex of the graph of the function [tex]\( y = x^2 - 4x + 3 \)[/tex] is at the point [tex]\((2, -1)\)[/tex].
Therefore, the correct option is:
A. [tex]\((2, -1)\)[/tex]
