Evidence of Understanding

**analyze quadratic expressions or equations and justify whether they are equivalent**- compare characteristics of each quadratic to determine if they model the same function
- substitute specific values into both equations, evaluate the equations, and justify equivalency
- consider how many input and output pairs suffice to show equivalency

- create diagrams or
**area**models to determine if two quadratics in factored, standard, or vertex form are equivalent*Example: use algebra tiles to represent x*^{2}+ 2x + 5 and (x + 1)^{2}+ 4 and determine whether the same set of tiles can be reorganized to represent each expression

- algebraically prove equivalency by representing each equation identically
- use the
**distributive property**to show two representations are equivalent,*Example: show (x - 5)(x - 2) is equivalent to any order of x*^{2}- 5x - 2x + 10 - relate factored form and standard form using properties of
**exponents**,*Example: x·x = x*^{2}, x·x^{2}= x^{3}, x^{2}·x^{2}= x^{4}, x^{50}**·**x^{32}= x^{82}, etc. - fluently add, subtract, or multiply polynomial expressions in the context of a situation

- use the

**create equivalent quadratic equations or expressions and justify equivalency**- given the factored or vertex form of a quadratic, write the equivalent standard form
- factor out the
**greatest common monomial factor**for any polynomial - use properties of exponents to factor a
**trinomial**of any even degree (especially degree 2 or 4)- recognize and justify when a trinomial cannot be factored into two
**binomials** *Example: recognize x*^{6}- 5x^{3}+ 6 as (x^{3})^{2}- 5x^{3}+ 6 and (x^{3}- 2)(x^{3}- 3)

- recognize and justify when a trinomial cannot be factored into two
- distinguish and factor quadratics that are
**perfect squares**or a**difference of squares***Example: recognize x*^{2}+ 20x + 100 is a perfect square because the numbers that multiply to 100 and add to 20 are both 10 and the area model is a square with side lengths of x + 10*Example: see x*^{4}- y^{4}as the difference of squares (x^{2})^{2}- (y^{2})^{2}, and therefore as (x^{2}- y^{2})(x^{2}+ y^{2})

Develop conceptual understanding:

distributive property, area, polynomial, trinomial, binomial, monomial, factor, perfect square, difference of squares

Supporting terms to communicate:

function, quadratic, expression, equation, factored form, standard form, sum, product, exponent, equivalent, polynomial, coefficient, leading coefficient