what is the vertex of the graph of $g(x) = |x - 8| + 6$?

$(6, 8)$
$(8, 6)$
$(6, -8)$
$(-8, 6)$

Question

what is the vertex of the graph of $g(x) = |x - 8| + 6$?

$(6, 8)$
$(8, 6)$
$(6, -8)$
$(-8, 6)$

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": [ "Absolute Value Functions", "Vertex of Absolute Value Function" ], "new_concepts": [], "current_concepts": [ "Absolute Value Functions", "Vertex of Absolute Value Function", "Function Translations" ] } ## Identify the standard vertex form Using the *Absolute Value Functions* knowledge point $$ y = a|x - h| + k $$ ## Determine the vertex coordinates Using the *Vertex of Absolute Value Function* knowledge point $$ \begin{aligned} &g(x) = |x - 8| + 6\ &h = 8,\quad k = 6\ &\text{Vertex} = (h, k) = (8, 6) \end{aligned} $$

(A) $(6, 8)$

(B) $(8, 6)$

(C) $(6, -8)$

(D) $(-8, 6)$

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "Math.abs(x - 8) + 6", "latex": "|x - 8| + 6" }, 0, 16 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "g(x)", "withLabel": true } }, { "type": "point", "params": [ [8, 6] ], "properties": { "name": "Vertex (8, 6)", "size": 5, "strokeColor": "#F2557F", "fillColor": "#F2557F", "withLabel": true, "labelColor": "#F2557F" } } ], "timestamps": [0.5, 1.0] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Vertex of Absolute Value Function" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the standard vertex form

Determine the vertex coordinates

Answer: