Solving Quadratic Equations in MYP Year 5 Maths
Learn to solve quadratic equations in MYP Year 5 Maths using factorisation, the quadratic formula, and completing the square with clear method guides and tips.
What Makes an Equation Quadratic?
A quadratic equation contains an x² term as its highest power and takes the standard form ax² + bx + c = 0. In MYP Year 5 you are expected to solve quadratic equations using three distinct methods, and to choose the most efficient method depending on the equation.
Method 1: Factorisation
If the quadratic can be written as a product of two brackets, factorisation is the quickest method. For example, x² + 5x + 6 = 0 factorises to (x + 2)(x + 3) = 0, giving solutions x = −2 or x = −3. Practise identifying factor pairs and handling negative signs carefully. Not all quadratics factorise neatly — that is where the other methods come in.
Method 2: The Quadratic Formula
The formula x = (−b ± √(b² − 4ac)) / 2a works for any quadratic. Identify a, b, and c from the equation, substitute carefully, and evaluate both the + and − cases. The expression under the square root — the discriminant (b² − 4ac) — tells you how many real solutions exist: two if positive, one if zero, none if negative.
Method 3: Completing the Square
Completing the square rewrites ax² + bx + c in the form a(x + p)² + q. This method is algebraically demanding but reveals the vertex of the parabola directly and is sometimes required by the question. Practise it as a standalone skill before applying it to solve equations.
Common Mistakes
- Forgetting the ± in the quadratic formula and finding only one solution.
- Dividing through by x to simplify — this loses the solution x = 0.
- Sign errors when identifying b and c (especially with negative coefficients).
Practice Strategy
Solve the same quadratic using all three methods to check they give identical answers. This reinforces each method and helps you spot errors. For assessments, unless a method is specified, use the one you are most confident with.