a quadratic function has a line of symmetry at $x = -3$ and a zero at $4$.

what is the distance from the given zero to the line of symmetry?

what is the other zero of the quadratic function?

Question

a quadratic function has a line of symmetry at $x = -3$ and a zero at $4$.

what is the distance from the given zero to the line of symmetry?

what is the other zero of the quadratic function?

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Symmetry of Quadratic Zeros" ], "current_concepts": [ "Axis of Symmetry", "Quadratic Functions", "Symmetry of Quadratic Zeros" ] } ## Calculate the distance from the given zero to the line of symmetry $$ \begin{aligned} d &= |4 - (-3)| \ d &= |4 + 3| \ d &= 7 \end{aligned} $$ ## Find the other zero using symmetry $$ \begin{aligned} x_{\text{other}} &= -3 - d \ x_{\text{other}} &= -3 - 7 \ x_{\text{other}} &= -10 \end{aligned} $$ ## Question 1 7 ## Question 2 -10 { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Symmetry of Quadratic Zeros" ] }

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Question

Explanation:

Calculate the distance from the given zero to the line of symmetry

Find the other zero using symmetry

Answer:

Question 1

Question 2