the axis of symmetry for the graph of the function (f(x)=3x^2+bx+4) is (x = \frac{3}{2}). what is the value of (b)?

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-9
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Question

the axis of symmetry for the graph of the function (f(x)=3x^2+bx+4) is (x = \frac{3}{2}). what is the value of (b)?

-18
-9
9
18

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": [ "Axis of Symmetry" ], "new_concepts": [], "current_concepts": [ "Axis of Symmetry", "Quadratic Vertex" ] } ## Identify the given quadratic parameters Using the *Axis of Symmetry* knowledge point $$ \begin{aligned} &f(x) = ax^2 + bx + c \ &a = 3,\quad c = 4 \ &\text{Axis of symmetry: } x = \frac{3}{2} \end{aligned} $$ ## Apply the axis of symmetry formula Using the *Axis of Symmetry* knowledge point $$ \begin{aligned} &x = -\frac{b}{2a} \ &\frac{3}{2} = -\frac{b}{2(3)} \ &\frac{3}{2} = -\frac{b}{6} \end{aligned} $$ ## Solve for the coefficient b Using the *Axis of Symmetry* knowledge point $$ \begin{aligned} &3 \cdot 6 = -2b \ &18 = -2b \ &b = -9 \end{aligned} $$

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{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Axis of Symmetry" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given quadratic parameters

Apply the axis of symmetry formula

Solve for the coefficient b

Answer: