complete
$y = \sqrt{x - 3} + 2$
$y = \sqrt{x + 3} - 2$
done
intro
left and below the parent
right and above the parent
left and above the parent
right and below the parent
5 of 19

Question

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Square Root Transformations", "Horizontal Translation", "Vertical Translation" ], "new_concepts": [], "current_concepts": [ "Square Root Transformations", "Horizontal Translation", "Vertical Translation" ] } ## Analyze the first function Using the *Square Root Transformations*, *Horizontal Translation*, and *Vertical Translation* knowledge points $$ \begin{aligned} &y = \sqrt{x - 3} + 2\ &\text{Horizontal shift: } 3 \text{ units right (since } x \to x - 3\text{)}\ &\text{Vertical shift: } 2 \text{ units up (since } y \to y + 2\text{)}\ &\text{Direction relative to parent } y = \sqrt{x}\text{: right and above} \end{aligned} $$ ## Analyze the second function Using the *Square Root Transformations*, *Horizontal Translation*, and *Vertical Translation* knowledge points $$ \begin{aligned} &y = \sqrt{x + 3} - 2\ &\text{Horizontal shift: } 3 \text{ units left (since } x \to x + 3\text{)}\ &\text{Vertical shift: } 2 \text{ units down (since } y \to y - 2\text{)}\ &\text{Direction relative to parent } y = \sqrt{x}\text{: left and below} \end{aligned} $$ ## Question 1 For $y = \sqrt{x - 3} + 2$, the graph is: **right and above the parent** ## Question 2 For $y = \sqrt{x + 3} - 2$, the graph is: **left and below the parent** { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Square Root Transformations" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the first function

Analyze the second function

Answer:

Question 1

Question 2