find the vertex of the absolute value function $y = 1/2 |x - 2| - 1$.

$\bigcirc$ $(1/2, 2)$
$\bigcirc$ $(2, -1)$

Question

find the vertex of the absolute value function $y = 1/2 |x - 2| - 1$.

$\bigcirc$ $(1/2, 2)$
$\bigcirc$ $(2, -1)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Absolute Value Function", "Absolute Value Transformations" ], "new_concepts": [], "current_concepts": [ "Absolute Value Function", "Absolute Value Transformations", "Vertex Form Parameters" ] } ## Identify the standard vertex form of an absolute value function $$ y = a|x - h| + k $$ ## Extract the vertex coordinates from the given equation $$ \begin{aligned} &y = \frac{1}{2}|x - 2| - 1\ &h = 2,\quad k = -1\ &\text{Vertex: } (h, k) = (2, -1) \end{aligned} $$

(A) $(1/2, 2)$

(B) $(2, -1)$

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "0.5*Math.abs(x-2)-1", "latex": "y = \frac{1}{2}|x-2|-1" }, -6, 10 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "point", "params": [ [2, -1] ], "properties": { "name": "Vertex (2, -1)", "size": 4, "color": "#F2557F", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Absolute Value Transformations" ] }

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Question

Explanation:

Identify the standard vertex form of an absolute value function

Extract the vertex coordinates from the given equation

Answer: