HSF.IF.C.8

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

HSF.IF.C.8.aUse the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.HSF.IF.C.8.bUse the properties of exponents to interpret expressions for exponential functions.
Khan Academy Resources
Standard form reviewSolving quadratics by completing the squareSolving quadratics by factoring reviewForms of linear equations reviewFactoring quadratics in any formCompleting the square reviewFactoring quadratics: Difference of squaresFactoring quadratics: Perfect squaresFactoring by groupingFactoring by common factor reviewFactoring quadratics: leading coefficient = 1Factoring simple quadratics reviewFactoring quadratics: leading coefficient ≠ 1Solving quadratics by factoringParallel & perpendicular lines from equationQuadratics by factoring (intro)Convert linear equations to standard formCompleting the square (intermediate)Completing the squareDifference of squaresFactoring quadratics introDifference of squares introQuadratics by factoringFactor polynomials: quadratic methodsFactor polynomials: quadratic methods (challenge)Factor quadratics by groupingQuadratic word problems (standard form)Zeros of polynomials (with factoring)Interpret quadratic modelsSolve equations using structureCompleting the square (intro)Features of quadratic functionsSlope from equationFeatures of quadratic functions: strategyInterpret change in exponential models: changing unitsPerfect squares introCompare features of functionsInterpret change in exponential models: with manipulationFactoring quadratics with a common factorPerfect squaresFactoring quadratics as (x+a)(x+b) (example 2)Factoring perfect squaresWorked example: completing the square (leading coefficient ≠ 1)More examples of factoring quadratics as (x+a)(x+b)Intro to groupingCompleting the squareFactoring two-variable quadratics: groupingFactoring quadratics by groupingFactoring quadratics: common factor + groupingFactoring quadratics: negative common factor + groupingFactoring perfect squares: negative common factorFactoring difference of squares: two variables (example 2)Solving quadratics by factoringVertex & axis of symmetry of a parabolaFinding the vertex of a parabola in standard formIntro to linear equation standard formFactoring perfect squares: missing valuesPerfect square factorization introFactoring quadratics as (x+a)(x+b)Finding zeros of polynomials (example 2)Finding zeros of polynomials (2 of 2)Interpret quadratic models: Factored formInterpreting change in exponential models: changing unitsSolving quadratics using structureZeros of polynomials (with factoring): groupingFactoring difference of squares: shared factorsFactoring perfect squares: shared factorsDifference of squares introStrategy in factoring quadratics (part 1 of 2)Factoring difference of squares: analyzing factorizationFactoring difference of squares: leading coefficient ≠ 1Strategy in factoring quadratics (part 2 of 2)Interpreting change in exponential models: with manipulationComparing maximum points of quadratic functionsVertex form introductionForms & features of quadratic functionsFactoring two-variable quadratics: rearrangingSolving quadratics by factoring: leading coefficient ≠ 1Factoring quadratics with a common factorWorked examples: Forms & features of quadratic functionsComparing features of quadratic functionsInterpret quadratic models: Vertex formFactoring polynomials: common binomial factorQuadratic word problem: mosquitoesFinding features of quadratic functionsComparing functions: shared featuresFactoring completely with a common factorFinding zeros of polynomials (1 of 2)Factoring two-variable quadraticsZeros of polynomials (with factoring): common factorFactoring difference of squares: missing valuesConverting from slope-intercept to standard formWorked example: Rewriting & solving equations by completing the squareWorked example: Rewriting expressions by completing the square
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