To find the vertex of the quadratic function [tex]\( y = x^2 - 4x + 3 \)[/tex], we can use the formula for the vertex of a parabola given by [tex]\( y = ax^2 + bx + c \)[/tex]. The x-coordinate of the vertex can be found using the formula:
[tex]\[ h = -\frac{b}{2a} \][/tex]
For the given function [tex]\( y = x^2 - 4x + 3 \)[/tex]:
- [tex]\( a = 1 \)[/tex]
- [tex]\( b = -4 \)[/tex]
- [tex]\( c = 3 \)[/tex]
Let's calculate the x-coordinate of the vertex, [tex]\( h \)[/tex]:
[tex]\[ h = -\frac{b}{2a} = -\frac{-4}{2 \cdot 1} = \frac{4}{2} = 2 \][/tex]
Now that we have the x-coordinate [tex]\( h = 2 \)[/tex], we can find the y-coordinate by substituting [tex]\( x = 2 \)[/tex] back into the original function:
[tex]\[ y = (2)^2 - 4(2) + 3 \][/tex]
[tex]\[ y = 4 - 8 + 3 \][/tex]
[tex]\[ y = -1 \][/tex]
Therefore, the y-coordinate [tex]\( k \)[/tex] is -1.
So the vertex of the function [tex]\( y = x^2 - 4x + 3 \)[/tex] is:
[tex]\[ (h, k) = (2, -1) \][/tex]
The correct answer is:
B. [tex]\((2, -1)\)[/tex]
