# Quadratic Functions in Mathematics 20-1

Central concept: **Quadratic Functions**

## Connections

- Quadratic Functions (expressed as) -> Vertex Form
- Quadratic Functions (expressed as) -> Standard Form
- Quadratic Functions (has) -> Vertex
- Quadratic Functions (has) -> Axis of Symmetry
- Quadratic Functions (has) -> Direction of Opening
- Quadratic Functions (has) -> Domain and Range
- Quadratic Functions (has) -> Intercepts
- Vertex Form (reveals) -> Vertex
- Standard Form (identifies) -> Intercepts
- Quadratic Functions (leads to) -> Quadratic Equations
- Quadratic Functions (leads to) -> Quadratic Inequalities
- Quadratic Functions (used in) -> Systems of Equations
- Quadratic Functions (models) -> Real-World Applications

## Notes

- **Quadratic Functions**: Functions of the form y=ax²+bx+c or y=a(x-p)²+q analyzed for key characteristics [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), [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17777)
- **Vertex Form**: y=a(x-p)²+q where (p,q) is the vertex; reveals vertex and direction directly [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/17777)
- **Standard Form**: y=ax²+bx+c; used to identify intercepts and requires analysis for vertex [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17778)
- **Vertex**: Maximum or minimum point of the parabola; determined from both forms [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), [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17777)
- **Axis of Symmetry**: Vertical line x=p through the vertex; divides parabola into mirror halves [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), [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17777)
- **Direction of Opening**: Determined by sign of a; upward if a>0, downward if a<0 [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), [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17777)
- **Domain and Range**: Domain is all real numbers; range depends on vertex and direction of opening [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), [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17777)
- **Intercepts**: x-intercepts (zeros) and y-intercept; found algebraically or graphically [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), [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17777)
- **Quadratic Equations**: Equations of the form ax²+bx+c=0; solved by factoring, completing the square, or quadratic formula [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17779), [Resource](https://goa-cc-uat-aili-app-001.azurewebsites.net/library/resource/L2B8wqn5oUawLk4_WJDe0Q)
- **Quadratic Inequalities**: Inequalities involving quadratic expressions; solved using graphical and algebraic methods [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17782)
- **Systems of Equations**: Linear-quadratic and quadratic-quadratic systems solved algebraically and graphically [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/17780)
- **Real-World Applications**: Parabolic paths, trajectories, structures, and design problems modelled by quadratic functions [Resource](https://goa-cc-uat-aili-app-001.azurewebsites.net/library/resource/L-Uj1j9H4kypxiv587R6aA), [Resource](https://goa-cc-uat-aili-app-001.azurewebsites.net/library/resource/9Im-lhmbb0m3jiTVElTJ2A), [Resource](https://goa-cc-uat-aili-app-001.azurewebsites.net/library/resource/L2B8wqn5oUawLk4_WJDe0Q)

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*AILI word map · language en · model claude-haiku-4-5-20251001 · generated 2026-09-17 · id 13735076-3833-4789-8d98-e1cef6c650c0*

### 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/17776)
- 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/17780)
- 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)