find the $x$-coordinate of the vertex in $y = 3x^2 + 7x + 9$.

$x = \frac{7}{6}$

$x = -\frac{7}{6}$

Question

find the $x$-coordinate of the vertex in $y = 3x^2 + 7x + 9$.

$x = \frac{7}{6}$

$x = -\frac{7}{6}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Vertex of Quadratic Function", "Quadratic Vertex Formula" ], "current_concepts": [ "Vertex of Quadratic Function", "Quadratic Vertex Formula" ] } ## Identify coefficients of the quadratic equation $$ \begin{aligned} &y = ax^2 + bx + c \ &a = 3, \quad b = 7, \quad c = 9 \end{aligned} $$ ## Apply the vertex x-coordinate formula $$ \begin{aligned} &x = -\frac{b}{2a} \ &x = -\frac{7}{2(3)} \ &x = -\frac{7}{6} \end{aligned} $$

$x = 7/6$

$x = -7/6$

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

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QUESTION IMAGE

Question

Explanation:

Identify coefficients of the quadratic equation

Apply the vertex x-coordinate formula

Answer: