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

The answer

The axis of symmetry of f(x) = (x − 2)² + 1 is the vertical line x = 2. On a graph, that's the dashed line running straight up through the vertex — the correct choice is the parabola with a vertical line at x = 2.

Read it straight off vertex form

This function is already in vertex form, f(x) = a(x − h)² + k:

• The vertex is (h, k).
• The axis of symmetry is the vertical line x = h.

Here h = 2 and k = 1, so the vertex is (2, 1) and the axis of symmetry is x = 2. The axis always runs through the vertex, which you can see in the figure: the dashed line splits the parabola into two mirror halves.

Why the +1 is a trap

A common mistake is to think the +1 affects the axis. It doesn't. The k value (here +1) only slides the parabola up or down. It changes how high the vertex sits, not its left-right position — and the axis of symmetry is purely a left-right (x) thing. So the axis stays x = 2 whether the function is (x − 2)², (x − 2)² + 1, or (x − 2)² − 50.

Another trap is the sign of h. Because the form is (x − h), the value of h is the number that makes the parenthesis zero. (x − 2) → h = +2. If it were (x + 2), that's (x − (−2)), so h = −2 and the axis would be x = −2.

Check it with the standard-form formula

If you'd rather not use vertex form, expand and use x = −b / (2a):

(x − 2)² + 1 = x² − 4x + 4 + 1 = x² − 4x + 5

So a = 1, b = −4, and:

x = −b / (2a) = −(−4) / (2 · 1) = 4 / 2 = 2

Same result — x = 2. Both methods agree, which is a good way to check yourself on a test.