Completing the Square vs Quadratic Formula
Both methods solve quadratic equations, but each has situations where it works better. This guide compares them.
Quadratic Formula
Works for ALL quadratic equations ax²+bx+c=0. Just substitute a, b, c into x = (−b ± √(b²−4ac)) / 2a. Reliable but can be slow.
Tips
- Works every time
- Given on the formula sheet
- Be careful with negative b values
Completing the Square
Rewrites x²+bx+c as (x+p)²+q. Useful for finding turning points, sketching graphs, and solving when asked to give exact answers.
Tips
- Shows the turning point directly
- Required when question says 'complete the square'
- Half the coefficient of x, then square it
Which to Choose
If the question says 'complete the square', do that. If it says 'solve', either works — formula is faster. For turning points, completing the square is essential.
Tips
- 'Express in the form' → completing the square
- 'Solve' → either method works
- For graphs → completing the square
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Yes, all content is aligned with the Cambridge IGCSE Mathematics 0580 syllabus for 2025-2027.
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