Quadratic equations
A quadratic equation is one where the highest power of x is two, and that little two means we can have two answers, not just one. We start with the zero-product rule — the idea that unlocks factorising — then solve quadratics by factorising, including ones we must rearrange to equal zero first, difference-of-squares, and common-factor cases. Next comes the quadratic formula, our never-fails method, worked slowly with careful attention to signs and even a decimal answer. We complete the square, meet the discriminant that tells us how many real solutions to expect, and finish by forming a quadratic from a real area problem and solving it.
By the end you should be able to (NSSCO Mathematics 6.4):
- Solve quadratic equations given in factorised form using the zero-product (null-factor) rule
- Solve quadratic equations by factorising, rearranging to equal zero first where needed
- Solve quadratics that are a difference of two squares or that share a common factor
- Solve quadratic equations using the quadratic formula x = (−b ± √(b² − 4ac)) / 2a, taking care with signs
- Solve quadratic equations by completing the square in the form (x + p)² + q
- Use the discriminant b² − 4ac to decide whether a quadratic has two, one, or no real solutions
- Form a quadratic equation from a problem, solve it, and reject any impossible answer
Miss Jay Jay and Mike talk through the whole topic — with the figure and working drawn live.