which graph represents the solution for $x^2 + x - 12 0$?

Question

which graph represents the solution for $x^2 + x - 12 > 0$?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations", "Function Inequalities" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Function Inequalities" ] } ## Find the boundary points of the inequality $$ \begin{aligned} &x^2 + x - 12 = 0 \ &(x + 4)(x - 3) = 0 \ &x = -4 \quad \text{or} \quad x = 3 \end{aligned} $$ ## Determine the solution intervals $$ \begin{aligned} &\text{For } x^2 + x - 12 > 0: \ &x < -4 \quad \text{or} \quad x > 3 \end{aligned} $$ ## Match the solution to the correct graph $$ \begin{aligned} &\text{Boundary points: } x = -4 \text{ and } x = 3 \text{ (open circles)} \ &\text{Shaded regions: } (-\infty, -4) \cup (3, \infty) \ &\text{This corresponds to the third graph.} \end{aligned} $$

(A) Shaded interval between -4 and 3 with open circles

(B) Shaded interval between -3 and 4 with open circles

(C) Shaded intervals pointing outwards from open circles at -4 and 3

(D) Shaded intervals pointing outwards from open circles at -3 and 4

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Function Inequalities" ] }

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QUESTION IMAGE

Question

Explanation:

Find the boundary points of the inequality

Determine the solution intervals

Match the solution to the correct graph

Answer: