Algebra 1 Teachers Weekly Assessment Package Units 10. Created by: Jeanette Stein & Phill Adams Algebra 1 Teachers

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1 Algebra 1 Teachers Weekly Assessment Package Units 10 Created by: Jeanette Stein & Phill Adams 2015 Algebra 1 Teachers

2 Contents SEMESTER 2 SKILLS...3 UNIT 10 - UNDERSTAND QUADRATIC FUNCTIONS...6 WEEK #25 - QUADRATICS AS FUNCTIONS...7 WEEK #26 - GRAPHING QUADRATICS...8 WEEK #27 - INTRODUCTION TO FACTORING...9 UNIT 10 - KEYS 10 WEEK #25 - QUADRATICS AS FUNCTIONS ANSWER KEY WEEK #26 - GRAPHING QUADRATICS ANSWER KEY WEEK #27 - INTRODUCTION TO FACTORING ANSWER KEY Semester 2 Skills Algebra 1 Weekly Assessments 2015 Algebra 1 Teachers

3 Algebra 1 Common Core Semester 2 Skills Week Unit CCSS Skill 18 7 F.LE.1b F.LE.1c Distinguish between linear and exponential function 18 7 F.LE.1a Prove that a function is either linear or exponential 18 7 F.BF.1a Write a function that describes a relationship between two quantities 19 7 F.IF F.BF F.LE.2 Recognize that sequences are functions, sometimes defined recursively Write arithmetic and geometric sequences both recursively and with an explicit formula Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs 20 8 A.SSE.1 Identify parts of an expression 20 8 F.IF.1 Identify a function and it s domain and range 20 8 F.IF.5 Find an appropriate domain given a context 20 8 F.IF.2 Evaluate exponential functions 21 8 N.RN.2 Change expressions using the rules of exponents 21 8 N.RN F.IF.8.b Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values Use the properties of exponents to interpret expressions for exponential functions F.BF.1.a Write a function that describes a relationship between two quantities F.IF.7.e Graph exponential functions and identify intercepts and end behavior 22 8 F.BF.3 Translate exponential functions 22 8 F.IF S.ID.6.a Compare the key components of a linear function graph to an exponential function graph. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. 3 Semester 2 Skills Algebra 1 Weekly Assessments 2015 Algebra 1 Teachers

4 Week Unit CCSS Skill 23 9 F.LE.1.a 23 9 F.LE.1.b F.LE.1.c 23 9 F.LE.3 Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals. Identify linear and quadratic functions Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function F.BF.1.b Combine functions using arithmetic 24 9 F.BF.1.b Understand situations using these combinations 24 9 F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context A.SSE.1.a Understand what the parts of a quadratic mean F.IF.1 Understand function, domain and range in terms of a quadratic function F.IF.2 Evaluate quadratic functions given a value of x in function notation F.BF.1.a Write an equation for a quadratic function given a relationship A.REI.10, F.IF.7.a & F.IF F.LE F.BF.3 Graph and create tables of quadratic functions and label key features Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Understand how to translate a quadratic function in a table, an equation or on a graph F.IF.8.a Factor simple quadratics F.IF.8.a Understand the concept and implications of a zero F.IF.9 Compare two quadratic functions to make decisions A.APR.1 Add, subtract, and multiply polynomials A.APR.1 & N.RN.3 Identify sets that are closed under operations and those that are not. 4 Semester 2 Skills Algebra 1 Weekly Assessments 2015 Algebra 1 Teachers

5 Week Unit CCSS Skill A.SSE.3a Factor quadratic equations A.SSE.3a Solve quadratic equations by factoring A.SSE.3b Complete the square F.IF.8 Use completing the square to find maximum and minumum values A.REI.4 Use the quadratic formula to solve quadratic equations A.REI.4 Be able to identify which process is best to solve a quadratic equation A.REI.7 Solve a system of equations containing one quadratic and one linear function 5 Semester 2 Skills Algebra 1 Weekly Assessments 2015 Algebra 1 Teachers

6 Unit 10 - Understand Quadratic Functions Weekly Assessments 6 Unit 10 - Understand Quadratic Functions Algebra 1 Weekly Assessments 2015 Algebra 1 Teachers

7 Week #25 - Quadratics as Functions 1. Identify the domain and range of the following graph. 2. The following expressions are equivalent. Which form most clearly identifies the vertex of the quadratic? Explain your reasoning. 1 2 x2 + 3x (x 1)(x 5) (x 3) Write the output, using function notation, of the following functions given the input of (1 x)(x 5) 2 a. f(x) = x 2 3x + 1 b. f(x) = x x 3 c. f(x) = 3 4 x2 + x 4 7 Unit 10 - Understand Quadratic Functions Algebra 1 Weekly Assessments 2015 Algebra 1 Teachers

8 Week #26 - Graphing Quadratics 1. Create a table of the function f(x) = 1 2 x2 + 3x 4 Be sure to choose two x-values that are right of the axis of symmetry and two x-values that are left of the axis of symmetry. You must identify the axis of symmetry, vertex, and y-intercept. Identify the x- intercepts if they are in your table. Explain how you know they are the x-intercepts. 2. Use the following graph to identify which graph appears to represent an exponential function. Explain your reasoning. x y 3. a. Describe how g(x) = 2x and h(x) = 2x 2 are different. b. Describe how both g(x) and h(x) compare to the function f(x) = x 2 8 Unit 10 - Understand Quadratic Functions Algebra 1 Weekly Assessments 2015 Algebra 1 Teachers

9 Week #27 - Introduction to Factoring 1. Factor each of the following and determine the zeros. a. f(x) = x 2 + 4x 5 2. Parabola A has x-intercepts at 2 and -4 with a y-intercept of -5. Whereas parabola B is modeled by the function g(x) = x 2 4x + 6. Which parabola has the lowest vertex? b. f(x) = x 2 + x 6 c. f(x) = x 2 + 2x The height vs time graph of object 1 is given in the graph below. The height of object 2 is given by the function h 2 (t) = 2.5t Which object reaches its maximum height first? 9 Unit 10 - Understand Quadratic Functions Algebra 1 Weekly Assessments 2015 Algebra 1 Teachers

10 Unit 10 - KEYS Weekly Assessments 10 Algebra 1 Weekly Assessments 2015 Algebra 1 Teachers

11 Week #25 - Quadratics as Functions Answer Key 1. Identify the domain and range of the following graph. 2. The following expressions are equivalent. Which form most clearly identifies the vertex of the quadratic? Explain your reasoning. 1 2 x2 + 3x 2.5 Standard form 1 (x 1)(x 5) 2 Intercept form 1 2 (x 3)2 + 2 Vertex form 1 (1 x)(x 5) Intercept form 2 Domain: -2 x 5 Range: -1 y Write the output, using function notation, of the following functions given the input of -2. a. f(x) = x 2 3x + 1 The third option is written in vertex form of f(x) = a(x h) 2 + k and is easiest to identify the vertex of (3, 2) f( 2) = ( 2) 2 ( 2) + 1 f( 2) = f( 2) = 9 ( 2, 9) b. f(x) = x x 3 f( 2) = ( 2) ( 2) 3 2 f( 2) = f( 2) = 8 ( 2, 8) c. f(x) = 3 4 x2 + x 4 f( 2) = 3 4 ( 2)2 + ( 2) 4 f( 2) = f( 2) = 3 ( 2, 3) 11 Unit 10 - KEYS Algebra 1 Weekly Assessments 2015 Algebra 1 Teachers

12 Week #26 - Graphing Quadratics Answer Key 1. Create a table of the function f(x) = 1 2 x2 + 3x 4 Be sure to choose two x-values that are right of the axis of symmetry and two x-values that are left of the axis of symmetry. You must identify the axis of symmetry, vertex, and y-intercept. Identify the x- intercepts if they are in your table. Explain how you know they are the x-intercepts. 2. Use the following graph to identify which graph appears to represent an exponential function. Explain your reasoning. x y The axis of symmetry is found by using = b 2a. The point (3, 0.5) is the vertex. This can be found by plugging the axis of symmetry back into the equation resulting in 0.5 as the y-value of the vertex. The y-intercept is the value of the function when x is 0. For this function, the y-intercept is -4. The x-intercepts can be found by looking the points that have an x-value of 0. For this function the points (2, 0) and (4, 0) are the x-intercepts Although graphs A and B are both curved upwards, graph B seems to be exponential due to its increase being greater than graph A. 3. a. Describe how g(x) = 2x and h(x) = 2x 2 are different. g(x) and h(x) open in opposite directions, the y-intercept of g(x) is 4 units higher than h(x). b. Describe how both g(x) and h(x) compare to the function f(x) = x 2 g(x) is vertically stretched (skinnier), opens the opposite direction and the y-intercept is shifted up 4 units when compared to f(x) h(x) is vertically stretched (skinnier), opens the same direction and has the same y-intercept when compared to f(x) 12 Unit 10 - KEYS Algebra 1 Weekly Assessments 2015 Algebra 1 Teachers

13 Week #27 - Introduction to Factoring Answer Key 1. Factor each of the following and determine the zeros. a. f(x) = x 2 + 4x 5 (x - 5)(x + 1) = 0 x = 5 and x = Parabola A has x-intercepts at 2 and -4 with a y-intercept of -5. Whereas parabola B is modeled by the function g(x) = x 2 4x + 6. Which parabola has the lowest vertex? By plotting the three points for parabola A and determining the vertex for parabola B, you can see that the vertex for parabola A is going to be lower than for parabola B. b. f(x) = x 2 + x 6 (x - 3)(x + 2) = 0 x = -2 and x = 3 2. The height vs. time graph of object 1 is given in the graph below. The height of object 2 is given by the function h 2 (t) = 2.5t Which object reaches its maximum height first? c. f(x) = x 2 + 8x 20 (x - 2)(x + 10) = 0 x = 2 and x = -10 The time object 1 reaches its maximum is about The time object 2 reaches its maximum is at 0. Therefore, object 2 reaches its maximum height first. 13 Unit 10 - KEYS Algebra 1 Weekly Assessments 2015 Algebra 1 Teachers