Generalization, model comparison, proof, and technology-assisted validation.
Directions: Show exact work before decimals, label domains or intervals, and explain calculator use.
1. {'id': 'u11-l06', 'number': 6, 'title': 'Hyperbolas and Asymptotic Structure', 'family': 'conics', 'week': 32, 'unit': 11, 'unit_title': 'Matrices, Systems & Conic Sections', 'essential': 'How do matrices, systems, and conic forms organize transformations, intersections, and geometric models?', 'project': 'Conic-and-Matrix Design System'}
Identify (x−2)²=8(y+1).
2. {'id': 'u11-l06', 'number': 6, 'title': 'Hyperbolas and Asymptotic Structure', 'family': 'conics', 'week': 32, 'unit': 11, 'unit_title': 'Matrices, Systems & Conic Sections', 'essential': 'How do matrices, systems, and conic forms organize transformations, intersections, and geometric models?', 'project': 'Conic-and-Matrix Design System'}
Find the center of (x+3)²/16+(y−2)²/9=1.
3. {'id': 'u11-l06', 'number': 6, 'title': 'Hyperbolas and Asymptotic Structure', 'family': 'conics', 'week': 32, 'unit': 11, 'unit_title': 'Matrices, Systems & Conic Sections', 'essential': 'How do matrices, systems, and conic forms organize transformations, intersections, and geometric models?', 'project': 'Conic-and-Matrix Design System'}
Find the semi-major axis of x²/25+y²/9=1.
4. {'id': 'u11-l06', 'number': 6, 'title': 'Hyperbolas and Asymptotic Structure', 'family': 'conics', 'week': 32, 'unit': 11, 'unit_title': 'Matrices, Systems & Conic Sections', 'essential': 'How do matrices, systems, and conic forms organize transformations, intersections, and geometric models?', 'project': 'Conic-and-Matrix Design System'}
Identify x²/9−y²/4=1.
5. {'id': 'u11-l06', 'number': 6, 'title': 'Hyperbolas and Asymptotic Structure', 'family': 'conics', 'week': 32, 'unit': 11, 'unit_title': 'Matrices, Systems & Conic Sections', 'essential': 'How do matrices, systems, and conic forms organize transformations, intersections, and geometric models?', 'project': 'Conic-and-Matrix Design System'}
State the asymptotes of x²/9−y²/4=1.
6. {'id': 'u11-l06', 'number': 6, 'title': 'Hyperbolas and Asymptotic Structure', 'family': 'conics', 'week': 32, 'unit': 11, 'unit_title': 'Matrices, Systems & Conic Sections', 'essential': 'How do matrices, systems, and conic forms organize transformations, intersections, and geometric models?', 'project': 'Conic-and-Matrix Design System'}
For y²=12x, find p.
7. {'id': 'u11-l07', 'number': 7, 'title': 'Conic Identification, Rotation & Applications', 'family': 'conics', 'week': 32, 'unit': 11, 'unit_title': 'Matrices, Systems & Conic Sections', 'essential': 'How do matrices, systems, and conic forms organize transformations, intersections, and geometric models?', 'project': 'Conic-and-Matrix Design System'}
Identify (x−2)²=8(y+1).
8. {'id': 'u11-l07', 'number': 7, 'title': 'Conic Identification, Rotation & Applications', 'family': 'conics', 'week': 32, 'unit': 11, 'unit_title': 'Matrices, Systems & Conic Sections', 'essential': 'How do matrices, systems, and conic forms organize transformations, intersections, and geometric models?', 'project': 'Conic-and-Matrix Design System'}
Find the center of (x+3)²/16+(y−2)²/9=1.
9. {'id': 'u11-l07', 'number': 7, 'title': 'Conic Identification, Rotation & Applications', 'family': 'conics', 'week': 32, 'unit': 11, 'unit_title': 'Matrices, Systems & Conic Sections', 'essential': 'How do matrices, systems, and conic forms organize transformations, intersections, and geometric models?', 'project': 'Conic-and-Matrix Design System'}
Find the semi-major axis of x²/25+y²/9=1.
10. {'id': 'u11-l07', 'number': 7, 'title': 'Conic Identification, Rotation & Applications', 'family': 'conics', 'week': 32, 'unit': 11, 'unit_title': 'Matrices, Systems & Conic Sections', 'essential': 'How do matrices, systems, and conic forms organize transformations, intersections, and geometric models?', 'project': 'Conic-and-Matrix Design System'}
Identify x²/9−y²/4=1.
11. {'id': 'u11-l07', 'number': 7, 'title': 'Conic Identification, Rotation & Applications', 'family': 'conics', 'week': 32, 'unit': 11, 'unit_title': 'Matrices, Systems & Conic Sections', 'essential': 'How do matrices, systems, and conic forms organize transformations, intersections, and geometric models?', 'project': 'Conic-and-Matrix Design System'}
State the asymptotes of x²/9−y²/4=1.
12. {'id': 'u11-l07', 'number': 7, 'title': 'Conic Identification, Rotation & Applications', 'family': 'conics', 'week': 32, 'unit': 11, 'unit_title': 'Matrices, Systems & Conic Sections', 'essential': 'How do matrices, systems, and conic forms organize transformations, intersections, and geometric models?', 'project': 'Conic-and-Matrix Design System'}
For y²=12x, find p.