Quadratic Equations
Solve by factorising (monic and non-monic), square roots, graphing, zero product property, completing the square (NEW v9), quadratic formula (MAJOR NEW v9), discriminant Δ=b²-4ac (NEW v9), simultaneous quadratic-linear (NEW v9).
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- 1Write in Standard Form ax² + bx + c = 0Rearrange equations into standard form by expanding and collecting terms.adaptive
- 2Discriminant Δ = b² - 4acUse the discriminant to determine the number and nature of roots.adaptive
- 3Identify Solutions (Roots) of a QuadraticCheck whether a given value is a root of a quadratic equation.adaptive
- 4Solve by Factorising (Monic)Solve monic quadratic equations by factorising into two linear factors.adaptive
- 5Solve by Factorising (Harder)Rearrange into standard form then factorise to solve quadratic equations.adaptive
- 6Solve by Taking Square RootsSolve equations of the form ax² = c by taking square roots.adaptive
- 7Solve Pure Quadratic (x² = c)Solve x² = c recognising two solutions x = ±√c.adaptive
- 8Solve (x + p)² = qSolve equations already written in perfect square form.adaptive
- 9Solve by Graphing (Identify x-intercepts)Identify the solutions to a quadratic from its graph as x-intercepts.adaptive
- 10Zero Product PropertyApply the zero product property: if (a)(b)=0 then a=0 or b=0.adaptive
- 11Solve Non-Monic Quadratics by FactorisingFactorise non-monic quadratics (ax²+bx+c) to find the roots.adaptive
- 12Complete the SquareRewrite a quadratic in completed square form (x+h)²+k.adaptive
- 13Solve by Completing the Square (Monic)Use completing the square to solve monic quadratics.adaptive
- 14Solve by Completing the Square (Non-Monic)Divide through by a, then complete the square to solve non-monic quadratics.adaptive
- 15Quadratic FormulaApply x = (-b ± √(b²-4ac)) / 2a to solve any quadratic equation.adaptive
- 16Simultaneous Quadratic-LinearFind the intersection points of a parabola and a straight line.adaptive