IP EMaths Notes (Upper Sec, Year 3-4): 06) Quadratic Functions and Graphs
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Complete the square, locate turning points, and sketch parabolas with intercepts and symmetry clearly marked.
Last updated 30 Nov 2025
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- Worked example - Sketch from completed square
- Worked example - Use the discriminant and quadratic formula
Q: What does IP EMaths Notes (Upper Sec, Year 3-4): 06) Quadratic Functions and Graphs cover?
A: Complete the square, locate turning points, and sketch parabolas with intercepts and symmetry clearly marked.
Start Here
| Read time | What to take away |
| 1 second | A quadratic graph is a parabola; its vertex and intercepts tell most of the story. |
| 10 seconds | Completed-square form gives the turning point quickly, the discriminant tells how many real roots exist, and the sign of the squared term shows whether the curve opens up or down. |
| 100 seconds | Work through the examples to connect algebra to the sketch: complete the square, mark the axis of symmetry, find intercepts, and use the turning point for maximum or minimum questions. |
Quadratic graphs model projectile paths, profit curves, and optimisation problems. Completing the square reveals turning points instantly and helps evaluate maxima or minima.
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These notes align with SEAB GCE O-Level Mathematics (4052) content used in IP programmes (exams from 2026).
Status: SEAB O-Level Mathematics 4052 syllabus (exams from 2026) checked 2025-11-30 - scope unchanged; remains the reference for these notes.
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