A1.9

Select an appropriate method to solve a quadratic equation in one variable.

A1.9.aUse the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Explain how the quadratic formula is derived from this form.A1.9.bSolve quadratic equations by inspection (such as x^2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation, and recognize that some solutions may not be real.
Khan Academy Resources
Understanding the quadratic formulaSolving quadratics by completing the squareSolving quadratics by factoring reviewQuadratic formula proof reviewCompleting the square reviewSolving simple quadratics reviewDiscriminant reviewSolving quadratics by taking square roots Quadratic formula reviewSolving quadratics by factoringQuadratic formulaQuadratics by factoring (intro)Completing the square (intermediate)Completing the squareQuadratics by factoringQuadratics by taking square rootsQuadratic word problems (standard form)Solve equations by completing the squareSolve equations using structureCompleting the square (intro)Quadratics by taking square roots (intro)Quadratics by taking square roots: with stepsQuadratics by taking square roots: strategyZero product propertyStrategy in solving quadraticsQuadratic word problem: ballWorked example: completing the square (leading coefficient ≠ 1)Worked example: quadratic formula (negative coefficients)Solving quadratics by taking square rootsCompleting the squareThe quadratic formulaSolving quadratics by factoringSolving quadratics by completing the square: no solutionWorked example: quadratic formula (example 2)Using the quadratic formula: number of solutionsSolve by completing the square: Non-integer solutionsSolving quadratics using structureSolve by completing the square: Integer solutionsZero product propertyStrategy in solving quadratic equationsSolving quadratics by taking square roots examplesSolving quadratics by taking square roots: with stepsSolving quadratics by factoring: leading coefficient ≠ 1Worked example: Rewriting & solving equations by completing the squareQuadratics by taking square roots: strategyWorked example: Rewriting expressions by completing the square
Goblins

1-on-1 AI tutoring aligned to A1.9. Instant help for students, real-time insights for teachers.

Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.

Free for teachers, forever →