Question

Helpppp Plsssss Asap!! Show your work!! Thank you!! ​

Answer 1

Hello!

The answer is: B) $(x-4)^{2}+1$

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).

$g(x)=(x-4)^{2}+1=x^{2}-8x+16+1=x^{2}-8x+17$

Where:

$a=1\\b=-8\\c=17$

Finding the vertex:

$x=\frac{-b}{2a}=\frac{-(-8)}{2*1}=\frac{8}{2}=4$

So, x-coordinate of the vertex is 4,

Susbtituting x into the function, we can find the y-coordinate

$g(4)=y=4^{2}-8(4)+17=1$

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!