Pass Check: Quadratic Equations
Solve equations with an x² term by factorising, formula or completing the square.
Quadratic equation
An equation of the form ax² + bx + c = 0 where a ≠ 0.
Roots
The values of x that make the quadratic equal zero, shown where the graph crosses the x-axis.
Discriminant
The value b² − 4ac, which tells you how many real roots the equation has.
Completing the square
Rewriting a quadratic as a(x + p)² + q to find the turning point or solve it.
Quick check
Mixed quiz
1. Solve x^2 - 9x + 18 = 0.
2. Use the quadratic formula to solve x^2 - 2x - 6 = 0, giving your answers to 2 decimal places.
3. Solve x^2 - 9x + 20 = 0.
4. Use the quadratic formula to solve x^2 - 2x - 8 = 0, giving your answers to 2 decimal places.
5. Which equation is a quadratic?
6. The turning point of y = (x-3)² + 5 is at which coordinates?
7. Solve x^2 - 8x + 16 = 0.
8. Use the quadratic formula to solve x^2 - 2x - 5 = 0, giving your answers to 2 decimal places.