Polynomials
Solving Quadratics: By Completing the Square

Polynomials

Quadratics​

• Factorising by sum and product {part 1}
• Factorising by sum and product {part 2}
• Factorising by cross method {part 1}
• Factorising by cross method {part 2}
• Solving quadratics: by factorisation
• Solving quadratics: by completing the square
• Solving quadratics: the quadratic formula
• The discriminant
• Sketching quadratics from factorised form
• Sketching quadratics from vertex form {part 1}
• Sketching quadratics from vertex form {part 2}
• Sketching quadratics by completing the square
• Sketching quadratics from general form
• Finding the quadratic function from its graph {part 1}
• Finding the quadratic function from its graph {part 2}
• Finding the quadratic function from its graph {part 3}
• Finding where functions meet

Student Questions

• Sketching quadratics by completing the square
• Where functions meet​

Cubics and Quartics

• Polynomial equality (equating coefficients)
• Factorising cubic polynomials
• Solving cubic polynomials
• Sketching cubic functions
• Finding cubic functions from its graph
• Sketching quartic functions
• ​Finding quartic functions from its graph​

Factorising quadratic expressions can be very difficult, especially when the solutions become irrational numbers. Quadratics with irrational solutions cannot be easily solved by factorisation, so instead a method called solution by completing the square can be used.