A1.A-REI.B.4.a
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – k)^2 = q that has the same solutions. Derive the quadratic formula from this form.
Example Problems
Convert to vertex form.
Convert to vertex form.
Convert to vertex form.
Khan Academy ResourcesUnderstanding the quadratic formulaSolving quadratics by factoring reviewQuadratic formula proof reviewCompleting the square 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)Features of quadratic functionsQuadratics by taking square roots: with stepsQuadratics by taking square roots: strategyZero product propertyQuadratic 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 rootsCompleting the squareThe quadratic formulaProof of the quadratic formulaSolving quadratics by factoringQuadratic equations word problem: box dimensionsSolving quadratics by completing the square: no solutionWorked example: quadratic formula (example 2)Using the quadratic formula: number of solutionsZero product propertySolving 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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