the graph of $g(x) = |x - h| + k$ is shown on the coordinate grid. what must be true about the values of $h$ and $k$?

both $h$ and $k$ must be positive.
both $h$ and $k$ must be negative.
$h$ must be positive and $k$ must be negative.
$h$ must be negative and $k$ must be positive.

Question

the graph of $g(x) = |x - h| + k$ is shown on the coordinate grid. what must be true about the values of $h$ and $k$?

both $h$ and $k$ must be positive.
both $h$ and $k$ must be negative.
$h$ must be positive and $k$ must be negative.
$h$ must be negative and $k$ must be positive.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Absolute Value Functions", "Vertex of Absolute Value Function" ], "new_concepts": [ "Vertex Coordinates Interpretation" ], "current_concepts": [ "Absolute Value Functions", "Vertex of Absolute Value Function", "Function Translations" ] } ## Identify the vertex from the graph Using the *Vertex of Absolute Value Function* knowledge point $$ \begin{aligned} &\text{Vertex } (x_v, y_v) \text{ lies in Quadrant II.}\ &x_v < 0\ &y_v > 0 \end{aligned} $$ ## Relate vertex to function parameters Using the *Absolute Value Functions* knowledge point $$ \begin{aligned} &g(x) = |x - h| + k\ &\text{Vertex is } (h, k) \end{aligned} $$ ## Determine the signs of h and k Using the *Vertex of Absolute Value Function* and *Absolute Value Functions* knowledge points $$ \begin{aligned} &h = x_v < 0 \implies h \text{ is negative.}\ &k = y_v > 0 \implies k \text{ is positive.} \end{aligned} $$ ## Match with the correct option Using the *Absolute Value Functions* knowledge point $$ \begin{aligned} &h \text{ must be negative and } k \text{ must be positive.} \end{aligned} $$

Both $h$ and $k$ must be positive.

Both $h$ and $k$ must be negative.

$h$ must be positive and $k$ must be negative.

$h$ must be negative and $k$ must be positive.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Absolute Value Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the vertex from the graph

Relate vertex to function parameters

Determine the signs of h and k

Match with the correct option

Answer: