Question

Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1?

Answer 1

$f(x)=(x-2)^2+1$

is symmetric around

$x=2$

a vertical line through (2,0)

Answer 2

Given function is

$f(x)=(x-2)^2+1$

Now question says to find the graph that shows the axis of symmetry for the given function.

Graph is missing but I can help you to find the correct graph.

Given equation is in the vertex form whose formula is given by

$f(x)=a(x-h)^2+k$

Comparing given function with above formula, we get:

a=1, h=2 and k=1.

For the vertex formula $f(x)=a(x-h)^2+k$, we know that axis of symetry is given by equation:

x=h

So for the given function, axis of symmetry will be x=2

Graph of x=2 will be a vertical line crossing x-axis at x=2

So you just need to find the graph from given choices which contains a vertical line crossing x-axis at x=2.