NC.M2.F-IF.8

Use equivalent expressions to reveal and explain different properties of a function by developing and using the process of completing the square to identify the zeros, extreme values, and symmetry in graphs and tables representing quadratic functions, and interpret these in terms of a context.

Example Problems

Convert

f(x) = x^2 + 6x + 8

to vertex form.

Convert

f(x) = x^2 - 2x - 20

to vertex form.

Convert

f(x) = 2x^2 - 4x - 1

to vertex form.

Khan Academy Resources

Factoring monomials Factoring polynomials by taking a common factor Factoring quadratics in any form Graphs of polynomials: Challenge problems Completing the square review Factoring quadratics: Difference of squares Zeros of polynomials & their graphs Factoring quadratics: Perfect squares Graphs of polynomials Factoring by grouping Factoring quadratics: leading coefficient = 1 Factoring quadratics: leading coefficient ≠ 1 Positive & negative intervals of polynomials Completing the square (intermediate)Completing the square Difference of squares Difference of squares intro Factor polynomials using structure Polynomial special products: perfect square Quadratic word problems (standard form)Zeros of polynomials (with factoring)Factor monomials Graph interpretation word problems Solve equations using structure Polynomial special products: difference of squares Identify quadratic patterns Factor polynomials: common factor Comparing linear functions word problems Interpret parabolas in context Interpret a quadratic graph Positive & negative intervals of polynomials Linear models word problems Completing the square (intro)Graphing linear relationships word problems Zeros of polynomials (multiplicity)Interpret time in exponential models Factor higher degree polynomials Linear equations word problems: graphs Equivalent forms of exponential expressions Interpret change in exponential models: changing units Perfect squares intro Quadratic word problems (vertex form)Interpret change in exponential models: with manipulation Factorization with substitution Interpret change in exponential models Zeros of polynomials (factored form)Perfect squares Quadratic word problems (factored form)GCF factoring introduction Connecting exponential graphs with contexts Factoring perfect squares Factoring using the difference of squares pattern Quadratic word problem: ball Worked example: completing the square (leading coefficient ≠ 1)Intro to grouping Completing the square Modeling with linear equations: snow Linear equations word problems: earnings Taking common factor from trinomial Factoring quadratics: common factor + grouping Factoring quadratics: negative common factor + grouping Factoring perfect squares: negative common factor Factoring using the perfect square pattern Solving quadratics by completing the square: no solution Finding the vertex of a parabola in standard form Linear graphs word problems Factoring perfect squares: missing values Polynomial special products: difference of squares Comparing linear functions word problem: work Perfect square factorization intro Factoring quadratics as (x+a)(x+b)Factoring higher-degree polynomials: Common factor Interpreting change in exponential models Interpreting change in exponential models: changing units Identifying perfect square form Linear functions word problem: iceberg Solving quadratics using structure Zeros of polynomials (with factoring): grouping Linear functions word problem: paint Multiplicity of zeros of polynomials Worked example: finding missing monomial side in area model Taking common factor: area model Linear functions word problem: pool Factoring difference of squares: shared factors Zeros of polynomials: matching equation to graph Factoring perfect squares: shared factors Comparing linear functions word problem: climb Quadratic word problems (vertex form)Interpreting time in exponential models Difference of squares intro Linear equations word problems: volcano Strategy in factoring quadratics (part 1 of 2)Zeros of polynomials: matching equation to zeros Factoring difference of squares: analyzing factorization Factoring difference of squares: leading coefficient ≠ 1 Strategy in factoring quadratics (part 2 of 2)Which monomial factorization is correct?Analyzing tables of exponential functions Interpreting change in exponential models: with manipulation Identifying quadratic patterns Vertex form introduction Linear graphs word problem: cats Quadratic word problems (factored form)Zeros of polynomials: plotting zeros Factoring with the distributive property Worked example: finding the missing monomial factor Taking common factor from binomial Graph interpretation word problem: temperature Factoring higher degree polynomials Polynomial special products: perfect square Factorization with substitution Analyzing graphs of exponential functions Comparing linear functions word problem: walk Zeros of polynomials (with factoring): common factor Linear functions word problem: fuel Analyzing graphs of exponential functions: negative initial value Zeros of polynomials (multiplicity)Zeros of polynomials introduction Reasoning about unknown variables: divisibility Graph interpretation word problem: basketball Worked example: Rewriting & solving equations by completing the square Reasoning about unknown variables Worked example: Rewriting expressions by completing the square Interpret a quadratic graph

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