Question

which of the following square root functions has the vertex (2, 3)?

\\(y = \sqrt{x - 2} + 3\\)

\\(y = \sqrt{x + 2} + 3\\)

Explanation:

Identify the vertex form of a square root function

$$ y = a\sqrt{x - h} + k $$

Determine the parameters for the given vertex

$$ (h, k) = (2, 3) \implies h = 2,\ k = 3 $$

Substitute parameters into the vertex form

$$ y = a\sqrt{x - 2} + 3 $$

Answer:

• (A) \(y = \sqrt{x - 2} + 3\) (Correct answer)
• (B) \(y = \sqrt{x + 2} + 3\)