Every quadratic can be solved by the formula, so the choice is about speed and about what else the question wants. Some questions insist on a particular method, and reading the wording first is part of the method.
Choosing a method
| Situation | Best method |
|---|---|
| Coefficients are small and factors are obvious | Factorise |
| Question says 'give answers to 2 d.p.' or 'in surd form' | Quadratic formula |
| Question asks for a turning point, minimum value or the form (x + a)² + b | Complete the square |
| Question says 'hence' after a completing-the-square part | Use that completed form |
Getting the formula right
Write the equation in the form ax² + bx + c = 0 before identifying a, b and c, and put brackets round negative values when substituting. Most formula errors are sign errors from skipping that step.
Completing the square, cleanly
- Factor out the coefficient of x² if it is not 1.
- Halve the coefficient of x and square it.
- Write the bracket and subtract the square you added.
- Simplify, then read off the turning point directly.
Whichever method you use, substitute at least one solution back into the original equation. It takes fifteen seconds and catches almost every slip.