value: 1

find the vertex of the function $y = \sqrt{x - 4} + 7$.

a. $(4, -7)$
b. $(4, 7)$
c. $(-4, 7)$
d. $(-4, -7)$

Question

value: 1

find the vertex of the function $y = \sqrt{x - 4} + 7$.

a. $(4, -7)$
b. $(4, 7)$
c. $(-4, 7)$
d. $(-4, -7)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Square Root Function" ], "new_concepts": [ "Vertex of Radical Function" ], "current_concepts": [ "Square Root Function", "Vertex of Radical Function" ] } ## Identify the standard form Using the *Square Root Function* knowledge point $$ y = a\sqrt{x - h} + k $$ ## Determine the vertex coordinates Using the *Square Root Function* knowledge point $$ \begin{aligned} &h = 4\ &k = 7\ &\text{Vertex} = (h, k) = (4, 7) \end{aligned} $$

a. (4, -7)

b. (4, 7)

c. (-4, 7)

d. (-4, -7)

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "Math.sqrt(x - 4) + 7", "latex": "\sqrt{x - 4} + 7" }, 4, 10 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "y = \sqrt{x-4}+7", "withLabel": true } }, { "type": "point", "params": [ [4, 7] ], "properties": { "name": "Vertex (4, 7)", "size": 5, "color": "#F2557F", "strokeColor": "#F2557F", "fillColor": "#F2557F", "withLabel": true } } ], "timestamps": [0.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Vertex of Radical Function" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the standard form

Determine the vertex coordinates

Answer: