three hundred yards of fencing is being used to fence in a rectangular garden. the area of the garden is modeled by a quadratic function of the rectangles width, $a(w)$. what does the second coordinate of the vertex of the quadratic function, $a(w)$, represent?

the minimum width that can be used for the fencing
the maximum area that can be enclosed by the fencing
the width that gives the maximum area
the length that gives the maximum area

Question

three hundred yards of fencing is being used to fence in a rectangular garden. the area of the garden is modeled by a quadratic function of the rectangles width, $a(w)$. what does the second coordinate of the vertex of the quadratic function, $a(w)$, represent?

the minimum width that can be used for the fencing
the maximum area that can be enclosed by the fencing
the width that gives the maximum area
the length that gives the maximum area

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Vertex of a Quadratic Function" ], "new_concepts": [], "current_concepts": [ "Vertex of a Quadratic Function", "Quadratic Functions" ] } ## Identify the variables and function coordinates $$ \begin{aligned} &\text{Input variable (first coordinate, } w\text{): width of the rectangular garden}\ &\text{Output variable (second coordinate, } A(w)\text{): area of the garden} \end{aligned} $$ ## Analyze the vertex of the quadratic function $$ \begin{aligned} &\text{Vertex coordinate form: } (w, A(w))\ &\text{Since area is maximized, the vertex represents the maximum point of the parabola } A(w)\ &\text{First coordinate } w\text{: the width that gives the maximum area}\ &\text{Second coordinate } A(w)\text{: the maximum area that can be enclosed} \end{aligned} $$

the minimum width that can be used for the fencing

the maximum area that can be enclosed by the fencing

the width that gives the maximum area

the length that gives the maximum area

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Vertex of a Quadratic Function" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the variables and function coordinates

Analyze the vertex of the quadratic function

Answer: