the axis of symmetry of a quadratic equation is $x = -3$. if one of the zeroes of the equation is 4, what is the other zero?

$\bigcirc$ -10
$\bigcirc$ -7
$\bigcirc$ -6
$\bigcirc$ -4

Question

the axis of symmetry of a quadratic equation is $x = -3$. if one of the zeroes of the equation is 4, what is the other zero?

$\bigcirc$ -10
$\bigcirc$ -7
$\bigcirc$ -6
$\bigcirc$ -4

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Symmetry of Quadratic Zeros" ], "new_concepts": [], "current_concepts": [ "Symmetry of Quadratic Zeros", "Zeros of Quadratic Functions", "Axis of Symmetry" ] } ## Set up the symmetry equation $$ \frac{x_1 + x_2}{2} = x_{\text{sym}} $$ ## Substitute the given values $$ \begin{aligned} x_1 &= 4 \ x_{\text{sym}} &= -3 \ \frac{4 + x_2}{2} &= -3 \end{aligned} $$ ## Solve for the other zero $$ \begin{aligned} 4 + x_2 &= -6 \ x_2 &= -10 \end{aligned} $$

(A) $-10$

(B) $-7$

(C) $-6$

(D) $-4$

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QUESTION IMAGE

Question

Explanation:

Set up the symmetry equation

Substitute the given values

Solve for the other zero

Answer: