A2.A.2.4: Recognize that a quadratic function has different equivalent representations [𝑓(𝑥) = 𝑎𝑥^2 + 𝑏𝑥 + 𝑐, 𝑓(𝑥) = 𝑎(𝑥 − ℎ)^2 + 𝑘, 𝑎𝑛𝑑 𝑓(𝑥) = 𝑎(𝑥 − 𝑝)(𝑥 − 𝑞)]. Identify and use the mathematical model that is most appropriate to solve problems.

Recognize that a quadratic function has different equivalent representations [𝑓(𝑥) = 𝑎𝑥^2 + 𝑏𝑥 + 𝑐, 𝑓(𝑥) = 𝑎(𝑥 − ℎ)^2 + 𝑘, 𝑎𝑛𝑑 𝑓(𝑥) = 𝑎(𝑥 − 𝑝)(𝑥 − 𝑞)]. Identify and use the mathematical model that is most appropriate to solve problems.

Example Problems

Convert

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

to vertex form.

Expand and combine like terms:

(9y^5 + 2)^2

Expand and combine like terms:

(2 - 7m^6)^2

Khan Academy Resources

Graphing quadratics review Quadratics by factoring (intro)Quadratics by factoring Graph quadratics in vertex form Quadratic word problems (standard form)Interpret quadratic models Number of solutions of quadratic equations Interpret a quadratic graph Features of quadratic functions Features of quadratic functions: strategy Quadratic word problems (factored form)Quadratic equations word problem: triangle dimensions Quadratic equations word problem: box dimensions Finding the vertex of a parabola in standard form Interpret quadratic models: Factored form Zero product property Quadratic word problems (vertex form)Comparing maximum points of quadratic functions Forms & features of quadratic functions Quadratic word problems (factored form)Solving quadratics by factoring: leading coefficient ≠ 1 Worked examples: Forms & features of quadratic functions Comparing features of quadratic functions Interpret quadratic models: Vertex form Finding features of quadratic functions

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