solve $x^2 - 6x + 5 0$ by looking at the graph.

Question

solve $x^2 - 6x + 5 > 0$ by looking at the graph.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Solving Quadratic Inequalities Graphically" ], "current_concepts": [ "Quadratic Inequalities", "Graphing Inequalities", "Solving Quadratic Inequalities Graphically" ] } ## Identify x-intercepts from the graph $$ x = 1 \quad \text{and} \quad x = 5 $$ ## Determine where the graph is above the x-axis $$ y > 0 \implies x < 1 \quad \text{or} \quad x > 5 $$ ## Express the solution in interval notation $$ (-\infty, 1) \cup (5, \infty) $$ $x < 1$ or $x > 5$ (or in interval notation: $(-\infty, 1) \cup (5, \infty)$) { "elements": [ { "type": "functiongraph", "params": [ { "js": "x*x - 6*x + 5", "latex": "x^2 - 6x + 5" }, -2, 8 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "y = x^2 - 6x + 5", "withLabel": true } }, { "type": "point", "params": [[1, 0]], "properties": { "name": "(1,0)", "color": "#F2557F", "size": 4, "withLabel": true } }, { "type": "point", "params": [[5, 0]], "properties": { "name": "(5,0)", "color": "#F2557F", "size": 4, "withLabel": true } } ], "timestamps": [0.5, 1.0] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Inequalities" ] }

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Question

Explanation:

Identify x-intercepts from the graph

Determine where the graph is above the x-axis

Express the solution in interval notation

Answer: