value: 1

find the vertex of the function $y = 3|x + 2| - 7$.

a. $(3, 7)$
b. $(2, -7)$
c. $(-2, -7)$
d. $(3, 2)$

Question

value: 1

find the vertex of the function $y = 3|x + 2| - 7$.

a. $(3, 7)$
b. $(2, -7)$
c. $(-2, -7)$
d. $(3, 2)$

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 of Absolute Value Function" ] } ## Identify the standard vertex form $$ y = a|x - h| + k $$ ## Compare the given function to standard form $$ \begin{aligned} &y = 3|x + 2| - 7 \ &y = 3|x - (-2)| + (-7) \end{aligned} $$ ## Extract the vertex coordinates $$ \begin{aligned} &h = -2 \ &k = -7 \ &\text{Vertex} = (h, k) = (-2, -7) \end{aligned} $$

a. (3, 7)

b. (2, -7)

c. (-2, -7)

d. (3, 2)

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "3*Math.abs(x + 2) - 7", "latex": "3|x + 2| - 7" }, -7, 3 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } }, { "type": "point", "params": [ [-2, -7] ], "properties": { "name": "Vertex (-2, -7)", "size": 5, "strokeColor": "#F2557F", "fillColor": "#F2557F", "withLabel": true, "labelPosition": [10, -10] } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Absolute Value Transformations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the standard vertex form

Compare the given function to standard form

Extract the vertex coordinates

Answer: