# Quadratic Functions Formative Quiz

*Time: 25 min. 6 questions.*

## Instructions

Answer each question in the space provided. Show all algebraic work for short answer and numeric questions, since partial credit depends on correct method. Where a question asks for a specific form (vertex, standard, factored), write your final answer in that form.

## Questions

1. For the quadratic function y = −2(x + 4)² − 3, state the coordinates of the vertex.

A) (4, −3)
B) (−4, −3)
C) (−4, 3)
D) (4, 3)

([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17777))

2. Determine the axis of symmetry and the direction of opening for the quadratic function y = 3x² − 12x + 7. Show the algebraic steps you use to find the axis of symmetry.

([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17778))

3. True or false: The trinomial 6x² + x − 2 factors as (3x − 2)(2x + 1).

([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17775))

4. The quadratic equation x² − 7x + 12 = 0 has two roots. Compute the value of the larger root.

([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17779))

5. For the quadratic function y = (x − 2)² + 5, state the range of the function.

A) y ≥ 5
B) y ≤ 5
C) x ≥ 2
D) All real numbers

([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17777))

6. Determine the x-intercepts of the quadratic function y = x² − x − 6 algebraically. State your answer as ordered pairs.

([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17778))

## Curriculum coverage

| Question | Outcome alias |
|---|---|
| 1 | [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17777) |
| 2 | [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17778) |
| 3 | [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17775) |
| 4 | [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17779) |
| 5 | [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17777) |
| 6 | [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17778) |

## Answer key

1. B) (−4, −3). In vertex form y = a(x − p)² + q, the vertex is (p, q); here p = −4 and q = −3.

2. Axis of symmetry x = 2, opening downward is incorrect since a = 3 > 0, so the parabola opens upward. Completing the square gives y = 3(x − 2)² − 5, so the axis of symmetry is x = 2 and the parabola opens upward.

3. False. Expanding (3x − 2)(2x + 1) gives 6x² + 3x − 4x − 2 = 6x² − x − 2, which does not match 6x² + x − 2.

4. 4. Factoring x² − 7x + 12 = 0 gives (x − 3)(x − 4) = 0, so the roots are x = 3 and x = 4, and the larger root is 4.

5. A) y ≥ 5. Since a = 1 > 0, the parabola opens upward with minimum value q = 5 at the vertex, so the range is y ≥ 5.

6. (3, 0) and (−2, 0). Factoring x² − x − 6 gives (x − 3)(x + 2) = 0, so x = 3 or x = −2, giving y = 0 at both values.

---
*AILI quiz · language en · model claude-sonnet-5 · generated 2026-09-17 · id a5487f66-8fb6-4e03-b278-86ac0a9c3fe7*

### 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/17777)
- 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/17778)
- 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/17780)
- 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/17781)
- 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/L2B8wqn5oUawLk4_WJDe0Q)
- resource:r3: Resources › type#studentsupport, type#teachersupport › MAT2791 (https://goa-cc-uat-aili-app-001.azurewebsites.net/library/resource/9Im-lhmbb0m3jiTVElTJ2A)