Hello!
The answer is: B) [tex](x-4)^{2}+1[/tex]
Why?
Since from the graph we can only see the position of the vertex (4,1), let's find the vertex of the chosen option (B).
[tex]g(x)=(x-4)^{2}+1=x^{2}-8x+16+1=x^{2}-8x+17[/tex]
Where:
[tex]a=1\\b=-8\\c=17[/tex]
Finding the vertex:
[tex]x=\frac{-b}{2a}=\frac{-(-8)}{2*1}=\frac{8}{2}=4[/tex]
So, x-coordinate of the vertex is 4,
Susbtituting x into the function, we can find the y-coordinate
[tex]g(4)=y=4^{2}-8(4)+17=1[/tex]
So, y-coordinate of the vertex is 1
Hence,
The Vertex is located at (4,1)
If the vertex is located at (4,1), then the chosen option is correct.
Have a nice day!
