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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Parabola Symmetry" ], "new_concepts": [ "Parabola Intercepts" ], "current_concepts": [ "Parabola Symmetry", "Parabola Intercepts" ] } ## Identify given values Using the *Parabola Symmetry* knowledge point $$ \begin{aligned} &\text{Vertex: } (h, k) = (-3, -4)\ &x_1 = 7 \end{aligned} $$ ## Apply axis of symmetry Using the *Parabola Symmetry* knowledge point $$ \begin{aligned} &x = h = -3\ &\frac{x_1 + x_2}{2} = h\ &\frac{7 + x_2}{2} = -3 \end{aligned} $$ ## Solve for other intercept Using the *Parabola Symmetry* knowledge point $$ \begin{aligned} &7 + x_2 = -6\ &x_2 = -13 \end{aligned} $$ The other $x$-intercept is $-13$. { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Parabola Symmetry" ] }

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Explanation:

Identify given values

Apply axis of symmetry

Solve for other intercept

Answer: