Hello Romom! To find the vertex, we can use the vertex formula to find x of the vertex and then use the equation to find the y of the vertex.
Vertex Formula: [tex]x = \frac{-b}{2a}[/tex]
[tex]y = x^2 - 4x + 6 [/tex]
b = (-4)
a = 1
[tex]x=\frac{-b}{2a}[/tex]
[tex]x=\frac{-(-4)}{2(1)}[/tex]
[tex]x=\frac{4}{2}[/tex]
[tex]x=2[/tex]
So the vertex x point is at 2 so (x,y) = (2,y)
Now lets find the y by inserting 2 where the x is located in the equation:
[tex]y = x^2 - 4x + 6[/tex]
[tex]y = 2^2 - 4(2) + 6[/tex]
[tex]y = 4 - 8 + 6[/tex]
[tex]y = 2[/tex]
Now that we found the y for the vertex, we have (x,y) = (2,2) and (2,2) is our vertex. We can graph the equation to and see (2,2) is correct.
