The student will investigate and describe the function can be described on an interval as •A relationships among solutions of an equation, increasing, decreasing, or constant. zeros of a function, x-intercepts of a graph, and behavior describes a function as x approaches •End factors of a polynomial expression. positive and negative infinity. zero of a function is a value of x that makes equal •A Prerequisite/Extension SOL zero. 7.13 a) verbal expressions as algebraic the domain, range, zeros, and intercepts of •Identify expressions and sentences as equations and a function presented algebraically or graphically. vice versa; b) evaluate algebraic expressions the graph of a function, identify intervals on •Given 8.1 a) simplify numerical expressions 8.4 which the function is increasing and decreasing. evaluate algebraic expressions using order of the end behavior of a function. •Describe operations A.1 represent verbal quantitative The states Fundamental Theorem of Algebra that, including complex and repeated situations algebraically/evaluate expressions for solutions, an degree polynomial equation nth given replacement values of variables 7.12 has exactly (solutions). n represent relationships with tables, graphs, rules, and words 8.17 ID domain, range 8.14 The following statements are equivalent: make connections between any two representations A.7 investigate/analyze is a zero of the polynomial function k f; function families and characteristics (x is a factor of k) f(x); – a)determine relation is function; is a solution of the polynomial k b)domain/range; c) zeros; d) x‐ and y equation = 0; and is an f(x) k x-intercept intercepts; e) find values of functions for for the graph of = y f(x). elements in domain; f) make connect the relationships among solutions of an •Describe between/among multiple representations of equation, zeros of a function, x-intercepts of a graph, functions and factors of a polynomial expression. a polynomial function, given its zeros. •Define a factored form of a polynomial •Determine expression from the x-intercepts of the graph of its corresponding function. a function, identify of multiplicity greater •For than 1 and describe the effect of those zeros on the graph of the function. a polynomial equation, determine the number of real solutions and nonreal solutions. Performance Task must be completed and graded on rubric by the end of Quarter 2
The student will investigate and describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression. Prerequisite/Extension SOL 7.13 a) verbal expressions as algebraic expressions and sentences as equations and vice versa; b) evaluate algebraic expressions 8.1 a) simplify numerical expressions 8.4 evaluate algebraic expressions using order of operations A.1 represent verbal quantitative situations algebraically/evaluate expressions for given replacement values of variables 7.12 represent relationships with tables, graphs, rules, and words 8.17 ID domain, range 8.14 make connections between any two representations A.7 investigate/analyze function families and characteristics a)determine relation is function; b)domain/range; c) zeros; d) x‐ and y intercepts; e) find values of functions for elements in domain; f) make connect between/among multiple representations of functions •A function can be described on an interval as increasing, decreasing, or constant. •End behavior describes a function as x approaches positive and negative infinity. •A zero of a function is a value of x that makes equal zero. •Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically. •Given the graph of a function, identify intervals on which the function is increasing and decreasing. •Describe the end behavior of a function. The Fundamental Theorem of Algebra states that, including complex and repeated solutions, an nth degree polynomial equation has exactly n (solutions). The following statements are equivalent: k is a zero of the polynomial function f; (x – k) is a factor of f(x); k is a solution of the polynomial equation f(x) = 0; and k is an x-intercept for the graph of y = f(x). •Describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression. •Define a polynomial function, given its zeros. •Determine a factored form of a polynomial expression from the x-intercepts of the graph of its corresponding function. •For a function, identify of multiplicity greater than 1 and describe the effect of those zeros on the graph of the function. a polynomial equation, determine the number of real solutions and nonreal solutions. Performance Task must be completed and graded on rubric by the end of Quarter 2
2014-2015_algebra2_completed_pacing_guide.docx