Alg2+Unit+3

===‍‍‍‍‍‍‍‍‍‍=== || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**=== 1. Make sense of problems and perseveres in solving them. 2. Reasons abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity and repeated reasoning. || Remembering Understanding Applying Analyzing Evaluating Creating || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**===
 * ===**Common Core Standard(s)**===
 * A-SSE.3.** Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★
 * **b.** Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
 * A-CED.2**. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
 * A-REI.11**. Explain why the //x//-coordinates of the points where the graphs of the equations //y// = //f//(//x//) and //y// = //g//(//x//) intersect are the solutions of the equation //f//(//x//) = //g//(//x//); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where //f//(//x//) and/or //g//(//x//) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★
 * A-APR.1.** Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
 * A-APR.2**. Know and apply the Remainder Theorem: For a polynomial //p//(//x//) and a number //a//, the remainder on division by //x – a// is //p//(//a//), so //p//(//a//) = 0 if and only if (//x – a//) is a factor of //p//(//x//).
 * A-APR.3.** Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
 * A-REI.4**.Solve quadratic equations in one variable.
 * Use the method of completing the square to transform any quadratic equation in //x// into an equation of the form (//x// – //p//)2 = //q// that has the same solutions. Derive the quadratic formula from this form.
 * Solve quadratic equations by inspection (e.g., for //x//2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as //a// ± //bi// for real numbers //a// and //b//.
 * F-IF.7**. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★
 * **c**. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
 * A.APR.4**. Prove polynomial identities and use them to describe numerical relationships. //For example, the polynomial identity (x2 + y2)2 = (x2 - y2)2 + (2xy)2 can be used to generate Pythagoren triples.//
 * A.APR.5**. (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive interger n, where x and y are numbers, with coefficients determined for example by Pascal's Triangle.
 * F-IF.8.**Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
 * **a**. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
 * F-BF.3**. Identify the effect on the graph of replacing //f//(//x//) by //f//(//x//) + //k//, //k// //f//(//x//), //f//(//kx//), and //f//(//x// + //k//) for specific values of //k// (both positive and negative); find the value of //k//given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
 * A-SSE.1**. Interpret expressions that represent a quantity in terms of its context.★
 * Interpret parts of an expression, such as terms, factors, and coefficients.
 * Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
 * A-SSE.2**. Use the structure of an expression to identify ways to rewrite it. //For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).//
 * N-CN.1.** Know there is a complex number //i// such that //i//2 = –1, and every complex number has the form //a + bi// with //a// and //b// real.
 * N-CN.2**. Use the relation //i//2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
 * N-CN.7**. Solve quadratic equations with real coefficients that have complex solutions.
 * N.CN.8**. (+) Extend polynomial identities to the complex numbers. //For example, rewrite x2 + 4 as (x +2i)(x - 2i).//
 * N-CN.9**. (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**=== || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking**===

**I can...**

 * Complete the square in a quadratic to find the max or min
 * Create equations in two or more variables
 * Graph equations in coordinate axes
 * Find the solutions to an equation in two variables that are contained on the graph of that equation
 * Find the solution by using technology to find the intersection of the functions
 * Add, subtract, and multiply polynomials
 * Apply the Remainder theorem
 * Understand roots of polynomials
 * Find the zeros of a polynomial
 * Use the zeros to sketch a graph
 * Write a quadratic equation in vertex form by completing the square
 * Derive the quadratic formula
 * Solve quadratic equations by factoring and completing the square to show the zeros
 * Define complex number
 * Graph functions and identify key features by hand or technology
 * Identify zeros and end behaviors by graphing functions
 * Prove polynomial identities
 * <span style="font-family: 'Tahoma','sans-serif'; font-size: 11px;">Use Pascal’s Triangle to find coefficients for expansion
 * <span style="font-family: 'Tahoma','sans-serif'; font-size: 11px;">Use the Binomial Theorem to find the nth term in expansion
 * <span style="font-family: 'Tahoma','sans-serif'; font-size: 11px;">Use factoring and completing the square to show zeros of a function
 * <span style="font-family: 'Tahoma','sans-serif'; font-size: 11px;">Graph functions and identify key features by hand or technology
 * <span style="font-family: 'Tahoma','sans-serif'; font-size: 11px;">Graph functions and identify key features by hand or technology
 * <span style="font-family: 'Tahoma','sans-serif'; font-size: 11px;">Identify the different parts of the expression and explain their meaning
 * <span style="font-family: 'Tahoma','sans-serif'; font-size: 11px;">Decompose expressions
 * <span style="font-family: 'Tahoma','sans-serif'; font-size: 11px;">Rewrite algebraic expressions in different equivalent forms
 * <span style="font-family: 'Tahoma','sans-serif'; font-size: 11px;">Define complex number
 * <span style="font-family: 'Tahoma','sans-serif'; font-size: 11px;">Apply the properties of complex numbers
 * <span style="font-family: 'Tahoma','sans-serif'; font-size: 11px;">Find a conjugate
 * <span style="font-family: 'Tahoma','sans-serif'; font-size: 11px;">Apply the Fundamental Theorem of Algebra

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**Essential Vocabulary**
complete the square, logarithmic function, system analogous, Remainder Theorem, zeros, factorization, Quadratic Formula, complex numbers, derive, Binomial Theorem, Pascal's Triangle, extreme values, Fundamental Theorem of Algebra

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Sample Assessments**=== ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Differentiation**===

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources**===

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===