Algebra · SS1–SS2

Quadratics & their graphs

Equations with x²: factorising, completing the square, the formula, and reading roots from a graph.

Before this: Linear & simultaneous equations
Leads to: Polynomials & algebraic division Calculus (JAMB bridge)Polynomials & quadratic roots

Learn

1The shape of a quadraticWhat y = ax² + bx + c looks like, what a, b and c each do to the curve, and why the roots are where it meets the x-axis.Done12 min
2Solving by factorisingTurn ax² + bx + c into two brackets, read off the roots, build the equation from its roots, and find the sum and product of the roots.Done16 min
3More factorisingDifference of two squares, factorising by grouping, quadratics in disguise (in √x or 3ˣ), and using factorising to simplify fractions and find where they are undefined.Done16 min
4Completing the squareRewrite x² + bx + c as a square plus a number. It solves any quadratic, finds the vertex, and is where the formula comes from.Done15 min
5The formula and the discriminantThe formula that solves any quadratic, what b² − 4ac tells you before you start, and how to set up quadratics from word problems.Done15 min
6The table-and-graph questionWAEC Paper 2's favourite quadratic question. Complete the table, draw the curve, then read roots, solutions and the turning point from it.Done15 min

Practise

Answer quadratics & their graphs questions one at a time. You'll know straight away whether you're right, with hints and the working step by step.

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Past questions (237)

From 1983–2025: 90 WAEC, 27 NECO, 120 JAMB. Theory questions first, then objective, newest first.

Theory (64)

Objective (173)