HSA.REI.B.4

Solve quadratic equations in one variable.

HSA.REI.B.4.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. Derive the quadratic formula from this form.HSA.REI.B.4.bSolve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
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 using structureNumber of solutions of quadratic equationsCompleting the square (intro)Quadratics by taking square roots (intro)Solve quadratic equations: complex solutionsQuadratics by taking square roots: with stepsQuadratics by taking square roots: strategyZero product propertyStrategy in solving quadraticsQuadratic equations word problem: triangle dimensionsQuadratic word problem: ballWorked example: completing the square (leading coefficient ≠ 1)Worked example: quadratic formula (negative coefficients)Solving quadratics by taking square rootsWorked example: quadratic formulaSolving quadratic equations: complex rootsSolving quadratics by taking square roots: challengeCompleting the squareThe quadratic formulaProof of the quadratic formulaSolving quadratics by factoringQuadratic equations word problem: box dimensionsSolving quadratics by completing the square: no solutionUsing the quadratic formulaWorked 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
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