what is the vertex of the graph of (f(x) = |x + 5| - 6)?

$(-6, -5)$
$(-6, 5)$
$(-5, -6)$
$(5, -6)$

Question

what is the vertex of the graph of (f(x) = |x + 5| - 6)?

$(-6, -5)$
$(-6, 5)$
$(-5, -6)$
$(5, -6)$

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", "Function Translations" ], "new_concepts": [], "current_concepts": [ "Absolute Value Functions", "Function Translations", "Vertex of Absolute Value Function" ] } ## Identify the standard vertex form Using the *Absolute Value Functions* knowledge point $$ y = a|x - h| + k $$ ## Determine the horizontal shift Using the *Function Translations* knowledge point $$ \begin{aligned} &x + 5 = x - (-5)\ &h = -5 \end{aligned} $$ ## Determine the vertical shift Using the *Function Translations* knowledge point $$ \begin{aligned} &k = -6 \end{aligned} $$ ## State the vertex coordinates Using the *Absolute Value Functions* knowledge point $$ (h, k) = (-5, -6) $$

(A) $(-6, -5)$

(B) $(-6, 5)$

(C) $(-5, -6)$

(D) $(5, -6)$

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QUESTION IMAGE

Question

Explanation:

Identify the standard vertex form

Determine the horizontal shift

Determine the vertical shift

State the vertex coordinates

Answer: