Quadratics
The Quadratic Formula

Quadratics

Factorising when A = 0

• Sum and product method (part 1)
• Sum and product method (part 2)

Factorising when A ≠ 0

• Cross method (part 1)
• Cross method (part 2)

Factorising special situations​

• Factorising perfect squares
• Factorising difference of two squares (part 1)
• Factorising difference of two squares (part 2)
• ​Factorising by completing the square​

Solving quadratic equations

• Solving basic quadratics
• Null factor law
• Solution by factorisation
• Solution by completing the square
• The quadratic formula

Sketching quadratic equations

• From factorised form
• From vertex form (part 1)
• From vertex form (part 2)
• By completing the square​​

Many quadratics cannot be easily solved by factorisation, and completing the square is a rather long and tedious process. Hence, a quadratic formula has been developed to assist with finding the solutions to any quadratic that has been given in unfactored form.
If \[ax^{2}+bx+c=0, a\neq 0\] Then \[x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\]