select the correct answer.

which equation represents this graph?

Question

select the correct answer.

which equation represents this graph?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Cubic Function Graphs", "Function Transformations" ], "current_concepts": [ "Cubic Functions", "Function Transformations", "Graph Intercepts" ] } ## Identify key features of the graph $$ \begin{aligned} &\text{Inflection point (center of symmetry): } (h, k) = (-1, 2)\ &\text{Y-intercept: } (0, 3)\ &\text{X-intercept: } (-2, 0) \end{aligned} $$ ## Determine the parent function and transformation form $$ \begin{aligned} &y = a(x - h)^3 + k\ &y = a(x + 1)^3 + 2 \end{aligned} $$ ## Solve for the vertical stretch factor $$ \begin{aligned} &3 = a(0 + 1)^3 + 2\ &3 = a(1) + 2\ &a = 1\ &y = (x + 1)^3 + 2 \end{aligned} $$ $y = (x + 1)^3 + 2$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Cubic Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Identify key features of the graph

Determine the parent function and transformation form

Solve for the vertical stretch factor

Answer: