# Quadratic Functions: Marking Guide (Mathematics 20-1, Grade 11)

## Task

Students present a labelled model or report on quadratic functions. The work demonstrates analysis of quadratic function characteristics, accurate graphing, and clear communication of mathematical reasoning.

## Curriculum alignment

Students are assessed on their ability to analyze quadratic functions of the form y = a(x − p)² + q and y = ax² + bx + c to identify vertex, domain and range, direction of opening, axis of symmetry, and x- and y-intercepts ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17777), [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17778)). Students apply these skills to solve problems involving quadratic functions ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17779)).

## Rubric

| Criterion | Beginning | Developing | Proficient | Exemplary |
|---|---|---|---|---|
| **Identification of function characteristics** | Identifies fewer than three characteristics (vertex, domain/range, direction of opening, axis of symmetry, intercepts) correctly. | Identifies three to four characteristics correctly; minor errors in calculation or interpretation. | Identifies all five characteristics correctly with accurate calculations and clear reasoning. | Identifies all characteristics correctly and explains how parameter changes (a, p, q or a, b, c) affect each feature. |
| **Graphing and labelling** | Graph is incomplete or missing key labels; points or features are inaccurate or unlabelled. | Graph shows most features; labels present but some are unclear or slightly misplaced. | Graph is accurate with all key features clearly labelled (vertex, intercepts, axis of symmetry). | Graph is precise and well-formatted; labels are positioned clearly; scale is appropriate and consistent. |
| **Mathematical communication** | Explanations are unclear or missing; notation is inconsistent or incorrect. | Explanations present but lack detail; notation is mostly correct with minor inconsistencies. | Explanations are clear and logical; mathematical notation is correct and used consistently throughout. | Explanations are thorough and precise; notation is correct; reasoning connects forms and features coherently. |
| **Problem solving and application** | Does not attempt to apply quadratic functions to a problem or application is incorrect. | Attempts application with partial understanding; some steps are missing or contain errors. | Applies quadratic functions to solve a problem; work is organized and mostly correct. | Applies quadratic functions to solve a problem efficiently; explains the relevance of findings and considers constraints or alternative approaches. |

## Scoring

Assign each criterion a level: Beginning = 1, Developing = 2, Proficient = 3, Exemplary = 4.

Sum the four criterion scores. Students are expected to analyze quadratic functions and determine their key characteristics. A score of 13 to 14 indicates strong proficiency; 15 to 16 indicates exemplary work. Use the overall score to assign a letter grade or percentage according to your school's grading scale.

## Notes for the teacher

- **Consistent interpretation of "correct":** Verify calculations independently. Minor rounding differences or equivalent forms (e.g., y = 2(x − 3)² + 5 and y = 2x² − 12x + 23) both count as correct.
- **Labelling standards:** Require axes labels, scale marks, and feature labels (vertex as an ordered pair, intercepts as points, axis of symmetry as a vertical line with its equation). Accept either form notation y = a(x − p)² + q or standard form y = ax² + bx + c; do not penalize the choice.
- **Problem-solving context:** If the task includes a real-world scenario (trajectory, profit, area), ensure the student's answer addresses the question asked and includes units or constraints where relevant.
- **Differentiation:** For support, provide a template with blanks for characteristics and a partially labelled graph. For extension, ask students to convert between forms, explain why a particular form is most useful for their problem, or compare two quadratic functions.

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*AILI marking guide · language en · model claude-haiku-4-5-20251001 · generated 2026-09-17 · id 0b659a77-0138-4c71-944c-42f7a7da3927*

### Sources

- node:n1: Mathematics › Mathematics (10–12) › Mathematics 20-1 › Relations and Functions › General Outcome (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17777)
- node:n2: Mathematics › Mathematics (10–12) › Mathematics 20-1 › Relations and Functions › General Outcome (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17776)
- node:n3: Mathematics › Mathematics (10–12) › Mathematics 20-1 › Relations and Functions › General Outcome (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17778)
- node:n4: Mathematics › Mathematics (10–12) › Mathematics 20-1 › Relations and Functions › General Outcome (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17777)
- node:n5: Mathematics › Mathematics (10–12) › Mathematics 20-1 › Relations and Functions › General Outcome (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17779)
- node:n6: Mathematics › Mathematics (10–12) › Mathematics 20-1 › Relations and Functions › General Outcome (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17775)
- node:n7: Mathematics › Mathematics (10–12) › Mathematics 20-1 › Relations and Functions › General Outcome (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17782)
- node:n8: Mathematics › Mathematics (10–12) › Mathematics 20-1 › Relations and Functions › General Outcome (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17780)
- node:n9: Mathematics › Mathematics (10–12) › Mathematics 20-1 › Relations and Functions › General Outcome (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17781)
- node:n10: Mathematics › Mathematics (10–12) › Mathematics 20-1 › Relations and Functions › General Outcome (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17776)
- resource:r1: Resources › type#studentsupport, type#teachersupport › MAT2791 (https://goa-cc-uat-aili-app-001.azurewebsites.net/library/resource/L-Uj1j9H4kypxiv587R6aA)
- resource:r2: Resources › type#studentsupport, type#teachersupport › MAT2791 (https://goa-cc-uat-aili-app-001.azurewebsites.net/library/resource/9Im-lhmbb0m3jiTVElTJ2A)
- resource:r3: Resources › type#studentsupport, type#teachersupport › MAT2791 (https://goa-cc-uat-aili-app-001.azurewebsites.net/library/resource/L2B8wqn5oUawLk4_WJDe0Q)
- resource:r4: Resources › type#studentsupport, type#teachersupport › MAT2791 (https://goa-cc-uat-aili-app-001.azurewebsites.net/library/resource/Ev9xj275wEyw23tOXVmz4w)
- resource:r5: Resources › type#studentsupport › MAT2791 (https://goa-cc-uat-aili-app-001.azurewebsites.net/library/resource/byh431Gvkk2zgLQtZNOBlA)