DUE: SEPTEMBER 13 TH, 2017

Transcription

1 Algebra 2 Summer Assignment 2017 Name: As an incoming Algebra 2 student, it is important that you are proficient in several skills from previous math courses. This assignment contains examples of the skills you are expected to know, such as factoring quadratic expressions, solving quadratic equations using different methods (factoring, square roots, and quadratic formula), adding polynomial expressions, subtracting polynomial expressions, and multiplying quadratic expressions, as you enter your Algebra II class in September. DUE: SEPTEMBER 13 TH, 2017 **Completion of this packet will count towards your first assessment grade** **All students entering Algebra 2 will be assessed on the skills reviewed in this assignment ** If you need assistance with any of these skills, we strongly recommend that you utilize the videos that are provided for each section. Enroll in the Franklin High School Math Department Google Classroom for easy access to hyperlinks using the code: 3ayq21k Or visit the Franklin Township Public Schools Mathematics page for more information: SCORING RUBRIC SCORE CRITERIA 5 Student completed packet and showed effort throughout. 3 Student partially completed packet and showed little effort throughout. 0 Student did not complete packet or showed no effort throughout.

2 Quadratic Expressions and Equations Factoring: Greatest Common Factor Resource: Factor out the Greatest Common Factor from each of the following expressions 1) 8x x 2) 6n 2 30n ) 18p 3 63p 2 9p Factoring Quadratic Expressions When a = 1 Resource: Factor the following expressions. 4) x x ) x 2 11x ) x 2 + 6x 16 Factoring Quadratic Expressions When a > 1 Resources: 1/factor-by-guess-and-check 1/factor-by-a-c-method 1/trinomial-possible-factors Factor the following expressions: 7) 2x 2 + 5x + 3 8) 4x 2 + 3x 7 9) 6x 2 11x + 4

3 Solving Quadratic Equations by FACTORING: Resource: Examples: Solve each of the following equations by FACTORING. 10) x 2 + 8x + 15 = 0 11) 3x 2 16x 7 = 5 12) 6x 2 13x + 3 = -3 Solving Quadratic Equations Using SQUARE ROOTS: Resource: Solve each of the following equations using SQUARE ROOTS. 13) 4x 2 6 = 74 14) 4(x 1) 2 5 = 223

4 Solving Quadratic Equations Using the QUADRATIC FORMULA: Resource: Solve the following equations using the QUADRATIC FORMULA x =!!±!!!!!"!! 15) 4x x 20 = 0 16) x 2 3x = 3 17) 4x 2 1 = -8x Polynomial Operations Adding Polynomial Expressions Resource: Add the following expressions. 18) (12y y 4) + (9y 2 13y + 3) = 19) (-7x x) + (10x 4 + 7x + 5x 5 ) Subtracting Polynomial Expressions Resource: Subtract the following expressions. 20) (3x 2 8x + 5) (8x 2 2x + 1) 21) (3 6n 5 8n 4 ) - (-6n 4 3n 8n 5 )

5 Multiplying Polynomial Expressions Resource: Multiply each of the following expressions. 22) 6x 2 (4x 2 + 5x 6) 23) (4x + 5)(2x 1) 24) (3x + 2)(5x 2 8x + 2) Apply Operations of Polynomials Resource: Farmer Bob is planting a garden this spring. He wants to plant squash, pumpkins, corn, beans, and potatoes. His plan for the field layout in feet is shown in the figure below. Use the figure and your knowledge of polynomials, perimeter, and area to solve the following: 1. Write and simplify an expression that represents the length of the south side of the field. 2. Write and simplify a polynomial expression that represents the perimeter of the pumpkin field.

6 3. Write and simplify a polynomial expression that represents the area of the potato field. 4. Write and simplify the polynomial expression that represents the area of the bean field if x = 3 and y = 7. What unit would the area of Bob s bean field have? Application of Quadratic Functions Click on the Link to watch the video --> Punkin Chunkin How long does a Projectile Pumpkin stay in the air? Directions: Watch the video and follow along to solve a problem that will tell us how long a Projectile Pumpkin will stay in the air. Answer the following questions as you go along. You may pause and re-watch the video as necessary. When you have finished the video and the related problem, see if you can use your skills to solve an additional pumpkin related problems. Problem 1: The graph of a Projectile Pumpkin may look like the graph below. The projectile s height over time can be described by the following quadratic equation where h = height and t = time. h = -16t t + 20

7 Based on the video and using the equation above, can you answer the following questions about the equation: 1. What is the initial velocity (related to the acceleration of gravity) of the pumpkin? 2. What is the initial upward velocity? 3. What is the initial height? 4. How long will the pumpkin stay in the air? To do this we must find the zero(s) or root(s) or solution(s) by FACTORING (Follow along with the video) Step 1 : Multiply by -1 Step 2: Divide by 4 Step 3: Ready to Factor ( t )( t ) = 0 Step 4: Set each Factor equal to zero and solve Step 5 : Using your answer from Step 4, Answer the Question How long does the pumpkin stay in the air before hitting the ground? Problem 2: 1: What is the maximum height the pumpkin reaches? 2: At what time does the pumpkin reach it s maximum height?

8 Problem 3: A pumpkin is launched from a catapult that is located at the top of a building that is 128 feet above the ground. The pumpkins height can be calculated after t seconds by the following Equation: h = -16t t How long will the pumpkin stay in the air? Factor the quadratic equation and solve.