Quadratic Equations Explained Simply

Quadratics have three solving methods, and students often panic because they don't know which to pick. Here's the simple decision tree.

Try factorising first

If the quadratic factorises neatly, this is the fastest route. Look for two numbers that multiply to the constant and add to the middle coefficient.

Use the formula when it doesn't factorise

The quadratic formula always works. If factorising isn't obvious within 30 seconds, switch to it rather than wasting time.

Complete the square for turning points

When a question asks for the minimum/maximum point or to "show that", completing the square is usually what's wanted.

Always check the discriminant

The part under the square root tells you how many real solutions exist — a common exam question in its own right.