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

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

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

Question

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

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

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Vertex of Radical Function", "Square Root Transformations" ], "new_concepts": [], "current_concepts": [ "Vertex of Radical Function", "Square Root Transformations" ] } ## 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 $$ y = a\sqrt{x - 2} + 3 $$

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

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

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Vertex of Radical Function" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the vertex form of a square root function

Determine the parameters for the given vertex

Substitute parameters into the vertex form

Answer: