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1 Know: Understand: Do: CC.2.1.HS.F.7 -- Essential Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems. CC.2.2.HS.D.4 -- Essential Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs. write and graph quadratic functions, solve quadratic equations using a variety of methods, perform operations with square roots and complex numbers CC.2.1.HS.F.7 -- Essential Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems. A Essential Simplify/write square roots in terms of i (e.g., 24 = 2i6). A Essential Simplify/evaluate expressions involving powers of i (e.g., i 6 + i 3 = 1 i). A Essential Add and subtract complex numbers (e.g., (7 3i) (2 + i) = 5 4i). A Essential Simplify/write square roots in terms of i (e.g., 24 = 2i6). A Essential Simplify/evaluate expressions involving powers of i (e.g., i 6 + i 3 = 1 i). A Essential Add and subtract complex numbers (e.g., (7 3i) (2 + i) = 5 4i). A Essential Multiply and divide complex numbers (e.g., (7 3i)(2 + i) = 17 + i). A Essential Write and/or solve quadratic equations (including factoring and using the Quadratic Formula). A Essential Multiply and divide complex numbers (e.g., (7 3i)(2 + i) = 17 + i). A Essential Write and/or solve quadratic equations (including factoring and using the Quadratic Formula). A Essential Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials limited to the form ax2+bx+c where a is not equal to 0. A a -- Essential Determine, use, and/or interpret minimum and maximum values over a specified interval of a graph of a function. A Essential Translate from one representation of a function to another (graph, table, and equation) Essential Make sense of problems and persevere in solving them Essential Reason abstractly and quantitatively. Page 1 of 5
2 Know: Understand: Do: A Essential Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials limited to the form ax2+bx+c where a is not equal to 0. A a -- Essential Determine, use, and/or interpret minimum and maximum values over a specified interval of a graph of a function. A Essential Translate from one representation of a function to another (graph, table, and equation) Essential Make sense of problems and persevere in solving them Essential Construct viable arguments and critique the reasoning of others Essential Model with mathematics Essential Use appropriate tools strategically Essential Attend to precision Essential Look for and make use of structure Essential Look for and express regularity in repeated reasoning. CC.2.1.HS.F.6 -- Essential Extend the knowledge of arithmetic operations and apply to complex numbers Essential Reason abstractly and quantitatively Essential Construct viable arguments and critique the reasoning of others Essential Model with mathematics Essential Use appropriate tools strategically Essential Attend to precision. Page 2 of 5
3 Know: Understand: Do: 7 -- Essential Look for and make use of structure Essential Look for and express regularity in repeated reasoning. CC.2.1.HS.F.6 -- Essential Extend the knowledge of arithmetic operations and apply to complex numbers. Page 3 of 5
4 Which standards are students learning in this unit? CC.2.1.HS.F.7 -- Essential Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems. CC.2.2.HS.D.4 -- Essential Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs. A Essential Simplify/write square roots in terms of i (e.g., 24 = 2i6). A Essential Simplify/evaluate expressions involving powers of i (e.g., i 6 + i 3 = 1 i). A Essential Add and subtract complex numbers (e.g., (7 3i) (2 + i) = 5 4i). A Essential Multiply and divide complex numbers (e.g., (7 3i)(2 + i) = 17 + i). A Essential Write and/or solve quadratic equations (including factoring and using the Quadratic Formula). A Essential Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials limited to the form ax 2 +bx+c where a is not equal to 0. A Essential Create, interpret, and/or use the equation, graph, or table of a polynomial function (including quadratics). A a -- Essential Determine, use, and/or interpret minimum and maximum values over a specified interval of a graph of a function. A Essential Translate from one representation of a function to another (graph, table, and equation). A Essential Identify or describe the effect of changing parameters within a family of functions (e.g., y = x 2 and y = x 2 + 3, or y = x 2 and y = 3x 2 ) Essential Make sense of problems and persevere in solving them. Page 4 of 5
5 2 -- Essential Reason abstractly and quantitatively Essential Construct viable arguments and critique the reasoning of others Essential Model with mathematics Essential Use appropriate tools strategically Essential Attend to precision Essential Look for and make use of structure Essential Look for and express regularity in repeated reasoning. CC.2.1.HS.F.6 -- Essential Extend the knowledge of arithmetic operations and apply to complex numbers. Page 5 of 5
6 Key Learning: graph and write quadratic functions, solve quadratic equations using a variety of methods, perform operations with square roots and complex numbers Unit Essential Question(s): How do you graph a parabola? What strategies are appropriate when solving a given quadratic equation? Concept: Concept: Concept: graph quadratic functions in graph quadratic functions in vertex standard form or intercept form A a, A A a, A solve by factoring, a=1 A , A , CC.2.2.HS.D.4 What is the shape and basic properties of the To graph a quadratic function, what are the How can factoring be used to solve a quadratic graph of a quadratic function? How is the advantages in having it written in vertex form or equation when a=1? How is the Zero-Product concept of minimum or maximum used in real world problems? (A) intercept form? (A) property used in solving equations? (A) quadratic function, parabola, vertex of a vertex form of a quardatic function, intercept monomial, binomial, trinomial, quadratic parabola, axis of symmetry, minimum value, form equation, root of an equation, zero of a function maximum value Concept: Concept: Concept: solve quadratic equations solve quadratic equations by finding complex numbers CC.2.2.HS.D.4, A , A square roots A A , A , A , A , CC.2.1.HS.F.6 How do you use factoring to solve a quadratic equation when a is not 1? (A) How do you use square roots to solve a quadratic equation? How do you simplify an expression with square roots? (A) How do you perform operations on complex numbers? Why do we need imaginary numbers? (A) standard form of a quadratic, zero of a function, square root, radical, radicand, rationalizing the imaginary number, complex number, "i", zero product property denominator, conjugates complex number plane, absolute value of a complex number, complex conjugates Page 1 of 2
7 Concept: Concept: Concept: complete the square quadratic formula graph and solve quadratic A , CC.2.2.HS.D.4 A , CC.2.1.HS.F.7 inequalities A , CC.2.2.HS.D.4 How is the process of completing the square used to solve quadratic equations? How do you find the number that is added to both sides of the equation to complete the square? (A) How do you use the quadratic formula and the discriminant? (A) How do you solve quadratic inequalities in one variable? What steps do you use to graph a quadratic inequality in two variables? (A) completing the square quadratic formula, discriminant quadratic inequality in two variables, quadratic inequality in one variable Additional Information: text, graphing calculator Attached Document(s): Page 2 of 2
8 Vocab Report for Concept: graph quadratic functions in standard form quadratic function - parabola - vertex of a parabola - axis of symmetry - minimum value - maximum value - Concept: graph quadratic functions in vertex or intercept form vertex form of a quardatic function - intercept form - Concept: solve by factoring, a=1 monomial - binomial - trinomial - quadratic equation - root of an equation - zero of a function - Concept: solve quadratic equations standard form of a quadratic - zero of a function - zero product property - Concept: solve quadratic equations by finding square roots square root - radical - radicand - rationalizing the denominator - conjugates - Concept: complex numbers imaginary number - complex number - "i" - complex number plane - absolute value of a complex number - complex conjugates - Page 1 of 2
9 Vocab Report for Concept: complete the square completing the square - Concept: quadratic formula quadratic formula - discriminant - Concept: graph and solve quadratic inequalities quadratic inequality in two variables - quadratic inequality in one variable - Page 2 of 2
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