analyze the graph of the cube root function shown on the right to determine the transformations of the parent function. then, determine the values of $a$, $h$, and $k$ in the general equation

\y = a\sqrt3{x-h}+k\

$h = \boxed{1}$

$k = \boxed{4}$

$a = \boxed{\quad}$

Question

analyze the graph of the cube root function shown on the right to determine the transformations of the parent function. then, determine the values of $a$, $h$, and $k$ in the general equation

\y = a\sqrt3{x-h}+k\

$h = \boxed{1}$

$k = \boxed{4}$

$a = \boxed{\quad}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Cube Root Transformations" ], "new_concepts": [], "current_concepts": [ "Cube Root Transformations", "Function Transformations" ] } ## Identify the inflection point (h, k) Using the *Cube Root Transformations* knowledge point $$ \begin{aligned} &\text{Inflection point on the graph: } (1, 4)\ &h = 1\ &k = 4 \end{aligned} $$ ## Substitute a known point to solve for a Using the *Cube Root Transformations* knowledge point $$ \begin{aligned} &y = a\sqrt[3]{x - h} + k \implies y = a\sqrt[3]{x - 1} + 4\ &\text{Identify another clear point on the graph: } (2, 6)\ &6 = a\sqrt[3]{2 - 1} + 4\ &6 = a(1) + 4\ &a = 2 \end{aligned} $$ Analyze the graph of the cube root function shown on the right to determine the transformations of the parent function. Then, determine the values of $a$, $h$, and $k$ in the general equation $y = a\sqrt[3]{x - h} + k$. $h =$ 1 $k =$ 4 $a =$ 2 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Cube Root Transformations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the inflection point (h, k)

Substitute a known point to solve for a

Answer: