Nc math 1 unit 7 building quadratic functions answer key

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1 NC Math 1 UNIT 7 Quadratics Functions Part

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3 MODULE 7 - TABLE OF CONTENTS QUADRATIC FUNCTIONS, Part Children s Barnyard - A Develop/Solidify Understanding Task Building and interpreting linear functions. (NC.M1.A-APR.1) READY, SET, GO Homework: Quadratic Functions Part Page Food at the Fair - A Practice Understanding Task Adding linear functions in context and out of context. (NC.M1.A-APR.1, NC.M1.F-IF.7NC.M1.F-BF.1b) READY, SET, GO Homework: Quadratic Functions Part Page Children s Barnyard Revisited - A Develop/Solidify Understanding Task Multiplying polynomials to find area. (NC.M1.A-APR.1, NC.M1.A-SSE.1b) READY, SET, GO Homework: Quadratic Functions Part Page Ages and Wages - A Practice Understanding Task Multiplying binomials. (NC.M1.A-APR.1, NC.M1.A-SSE.1b) READY, SET, GO Homework: Quadratic Functions Part Page Lines at the State Fair - A Develop Understanding Task Finding the second difference. (NC.M1.A-SSE.1b, NC.M1.A-CED.2) READY, SET, GO Homework: Quadratic Functions Part Page Homegrown Music Fest - A Solidify Understanding Task Finding a maximum. (NC.M1.A-SSE.1b, NC.M1.F-BF.1b, NC.M1.F-IF.4, NC.M1.F-IF.5, NC.M1.F-IF.7) READY, SET, GO Homework: Quadratic Functions Part Page 27

4 7.7 Circle C Racing Pigs - A Solidify Understanding Task Identifying key features of quadratics. (NC.M1.A-APR.3, NC.M1.F-IF.4, NC.M1.F-BF.1b) READY, SET, GO Homework: Quadratic Functions Part Page Nothing Could Be Finer - A Practice Understanding Task Identifying key features of quadratic functions in context while comparing multiple representations. (NC.M1.A-APR.3, NC.M1.A-CED.2, NC.M1.F-IF.4) READY, SET, GO Homework: Quadratic Functions Part Page 39

5 NC Math 1 Unit 7 Quadratic Functions 7.1 Children s Barnyard A Develop/Solidify Understanding Task The NC State Fair Planning Committee is working on the layout for the Children s Barnyard, which is an exhibit that allows fair visitors to get up close and personal with farm animals. Their plan for the layout is shown in the figure below. Measurements are in feet. d=&cad=rja&uact=8&ved=2ahukewiooi2ayl_cahwj 14MKHQmbBe8QjRx6BAgBEAU&url=https%3A%2F% 2Fwww.flickr.com%2Fphotos%2Ftaborroeder%2F &psig=AOvVaw2fRtliq6rDjo sxydisp6au&ust= Use your knowledge of geometric figures to find the perimeter of each animal pen. Page 1

6 NC Math 1 Unit 7 Quadratic Functions 2. What does x represent? 3. If x = 7, what is the perimeter of the sheep pen? 4. If the perimeter of the sheep pen is 100 feet, what is x? Page 2

7 NC Math 1 Unit 7 Quadratic Functions 7.1 READY Topic: Finding perimeter and area of figures Find the perimeter of each figure below. Page 3

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9 NC Math 1 Unit 7 Quadratic Functions Go! Topic: Finding rate of change Find the rate of change for each of the following functions y = x + 5 rate of change = 3 ( ) ( ) ( ) f 1 = 21, f n = f n rate of change = n f ( n) rate of change = rate of change = Page 5

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11 NC Math 1 Unit 7 Quadratic Functions 7.2 Food at the Fair A Practice Understanding Task At the NC State Fair, John is an owner of two food booths. One of his booths sells cotton candy and the other sells turkey legs. &cd=&cad=rja&uact=8&ved=2ahukewirus2rzb _cahwp34mkhz95cauqjrx6bagbeau&url=htt ps%3a%2f%2fen.wikipedia.org%2fwiki%2ffile %3AOhio_State_Fair_Picture_1.JPG&psig=AOv Vaw0pjBtigxLudCmqdk1850PF&ust= The cotton candy booth pays $500 per day for food materials and $16 per hour for people to work the booth. The permit and materials for the turkey leg booth costs $700 for the day and labor costs $30 per hour. Both booths are open for 12 hours a day. 1. Model the total amount the owner is spending each day to operate the two booths. Use multiple representations such as graphs, tables, and equations. 2. How much more does the turkey leg booth cost per day? Model the situation using multiple representations. 3. If cotton candy sells for $4 per bag, how many bags does the owner have to sell to break even? 4. If turkey legs sell for $5 per leg, how many turkey legs does he have to sell to break even? Page 7

12 NC Math 1 Unit 7 Quadratic Functions Given the functions below, find the sums. f(x) = 7x 9 g(x) = -2x + 1 h(x) = 3x + 5 j(x) = -x What is the sum of f(x) and g(x)? 6. What is the sum of h(x) and j(x)? 7. What is the sum of f(x) and j(x)? 8. What is the sum of g(x) and h(x)? 9. f(x) + h(x) =? 10. g(x) + j(x) =? Page 8

13 NC Math 1 Unit 7 Quadratic Functions 7.2 READY Topic: Add and subtract linear expressions Write an equivalent expression in the form ax + b. 3x + 5 2) ( 5 x - 2) + ( 7x + 8) + 8x + 7 1) ( x ) ( ) ( 3x - 2) - ( 5-3x) 3) x + 3 4) 5) Marcie is shopping for a movie streaming service. Flixnet charges a flat $4.50 per movie with no monthly membership fee. Choyko charges a monthly membership fee of $4, and then $3.25 per movie. a. Write a function to describe the total monthly cost for each service Flixnet: Choyko: b. Write an expression for the difference between the monthly costs for the two services. 6) Xian is planning to sell souvenirs at one of the upcoming county fairs. At the Walch County Fair, a vendor s permit would cost $75, and he could expect to pay his seller $9 per hour. At the Pickaway County Fair, a vendor s permit costs $60, but since the fair is busier and further away, he would have to pay his seller $11 per hour. a. Write a function to describe Xian s total costs for each fair Walch County Pickaway County Page 9

14 NC Math 1 Unit 7 Quadratic Functions 7.2 b. If Xian decides to send a seller to both fairs, write an expression for the total cost of permits and sellers for x hours i. What is the rate of change (total hourly wage cost) if Xian decides to send sellers to both fairs? c. Write an expression for the difference in the costs between the two fairs SET Topic: Combine linear functions and determine features of the graphs Given the functions for questions 7 & 8: f(x) = ' ( x + 2 7) Find f(x) + g(x) g(x) = - ( x + 5 8) How does the y-intercept of this new function compare to the y-intercept of each of the original functions? Given the functions: for questions 9 & 10: m(x) = 0 ' x + 3 p(x) = 0 ' x 4 9) What do you notice about the slopes of the linear functions given? What does this mean for their graphs? 10) Make a prediction: When you find the sum of these functions, what will the new graph look like? Specify what you think the y-intercept, the x-intercept, the slope will be. Page 10

15 NC Math 1 Unit 7 Quadratic Functions 7.2 GO! Topic: Write a linear equation based on a context Write an explicit linear equation to model the situations. 11) Sarah is going to put on a charity concert. She gets a total donation of $3,500 from her biggest supporter, and then also makes money when people purchase a ticket for $3 each. Write an equation for her total income depending on the number of tickets she sells. 12) Micah is a car salesperson who made $4,000 in commission this week. He also makes $9.50 per hour. Write an equation that represents the total amount of money made that week depending on the number of hours he worked. 13) Miraya is watching the concert venue fill up with people. The stadium holds 35,000 people and she notices that every minute 300 more people sit down. Write an equation that will help her predict how many seats will be still empty at any given minute. 14) Jamal and his friends are going to put on a concert. They have to pay $2,000 in start-up costs for their venue, electricity, security, and concessions. They will make $12 per ticket that they sell. Write an equation for their profit depending on the number of tickets sold. Page 11

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17 NC Math 1 Unit 7 Quadratic Functions 7.3 Children s Barnyard Revisited A Develop/Solidify Understanding Task The NC State Fair Planning Committee is still working on plans for the Children s Barnyard. They need to rebuild the barnyard using new dimensions. cd=&cad=rja&uact=8&ved=2ahukewjygq3j1l_cah WJzlMKHTD6AdoQjRx6BAgBEAU&url=https%3A% 2F%2Fwww.flickr.com%2Fphotos%2Ftaborroeder%2F &psig=AOvVaw30_y1TMt5 VINcO_HJD6Krf&ust= In order to begin, the Committee will start with the duck pen. Let x represent the dimensions of each side of the duck pen. x Duck Pen x 2. Now draw a diagram to represent the area of the cow pen if it starts at the same size as the duck pen, but is increased by 4 feet on one side and 3 on the other. 3. Continue to find the dimensions of each pen by drawing a diagram and writing expressions given the following scenarios. Use x to represent the length of the sides of the original square. a. Sheep pen is increased by 7 feet on one side and decreased by 2 on the other. Page 13

18 NC Math 1 Unit 7 Quadratic Functions b. Goat pen is decreased by 5 on one side and increased by 3 on the other. 4. Using your new dimensions of each pen, find the area of each new lot as the product of the length and width. 5. If x = 5, what would the area be for each pen? 6. Write an expression to represent the total area of the cow s pen and sheep s pen together. Page 14

19 NC Math 1 Unit 7 Quadratic Functions 7.3 READY Topic: Using Distributive Property and Exponent Rules to simplify. Simplify the following expressions. 1. (3x)(x 7) 2. x x x 3. x(x + 1) x(3x + 8) 4. (x x) (x 2 + x 3) 5. x(x + 12) 3(x 2 3) 6. (x 11) x(x + 2) SET Topic: Evaluating Functions Given the functions below, find the products identified. f(x) = 7x 9 g(x) = 2x + 1 h(x) = 3x + 5 j(x) = x What is the product of f(x) and g(x)? Page 15

20 NC Math 1 Unit 7 Quadratic Functions What is the product of h(x) and j(x)? 9. What is the product of f(x) and j(x)? 10. g(x) h(x) 11. f(x) h(x) 12. (g(x))(j(x)) GO! Topic: Evaluate a quadratic function for a given value of x The graph to the right f(x) represents a ball being shot straight up in the air from the ground, traveling up through the air, and then coming back down. 13. What is f(0) in this graph? 14. What does f(0) represent? 15. What is f(5) in this graph? 16. What does f(5) represent? 17. What is f(10) in this graph? 18. What does f(10) represent? Page 16

21 NC Math 1 Unit 7 Quadratic Functions 7.3 Evaluate the functions f(x) = 2x 2 3x + 9 and g(x) = 3x 2 + 8x 1 for the given values of x. 19. What is f(3)? 20. What is g( 2)? 21. What is f( 5)? 22. What is g(8)? 23. What is f(0)? 24. What is g(0)? Page 17

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23 NC Math 1 Unit 7 Quadratic Functions 7.4 Ages and Wages A Practice Understanding Task 1. Edgar is six years older than Patty, and Isabella is two years younger than Patty. Write two expressions for the product of Edgar and Isabella s age, based on Patty s unknown age. cd=&cad=rja&uact=8&ved=2ahukewivjij589vcahu QS60KHe5RC54QjRx6BAgBEAU&url=https%3A% 2F%2Ftorange.biz%2Fillegal-wages-envelope- dollars-4710&psig=aovvaw1hxzoqdv4j5a- DVi_Q7Hhw&ust= Fran is twice Patty s age, and Roberto is four years less than three times Patty s age. Write two expressions for the product of Fran and Roberto s age, based on Patty s unknown age. 3. Write and simplify an expression that represents the sum of all of their ages, including Patty s, all based on Patty s unknown age. 4. Edgar makes $2 per hour more than Patty, and Isabella makes $0.50 less per hour than Patty. Write two expressions for the product of Edgar and Isabella s money that they make per hour, based on Patty s unknown wage. Page 19

24 NC Math 1 Unit 7 Quadratic Functions 5. Fran makes four times as much money as Patty does, and Roberto makes one dollar more than twice as much money as Patty. Write two expressions for the product of Fran and Roberto s money that they make per hour, based on Patty s unknown wage. 6. Write and simplify an expression that represents the sum of all of their wages, including Patty s, all based on Patty s unknown wage. 7. If Patty is a 25 year old waitress who makes $8 per hour, find the ages and wages of all of her friends. Page 20

25 NC Math 1 Unit 7 Quadratic Functions 7.4 READY Topic: Graphing Quadratics. Using the quadratic function, complete the table and then graph. 1. y = x 2 4x 5 x y y = x 2 + 4x + 3 x y Page 21

26 NC Math 1 Unit 7 Quadratic Functions 7.4 SET Topic: Multiplying Polynomials. Simplify. 3. (3w + 4)(2w 1) 4. (y + 3) 2 5. (6x 11)(x + 3) 6. (d 2 + 1)(d 1) 7. (4x 6) 2 8. (x + y)(x y) GO! Topic: Solving Systems of Equations. Solve. 9. y = 3x 1 y = -2x x + 7y = 77 5x + 3y = x = -2y x = y x = 4y x + 2y 21 = 0 Page 22

27 NC Math 1 Unit 7 Quadratic Functions 7.5 Lines at the State Fair A Develop Understanding Task urce=images&cd=&cad=rja&uact=8 &ved=2ahukewirs6iy2b_cahvl0lm KHeSUC9gQjRx6BAgBEAU&url=htt ps%3a%2f%2fcommons.wikimedia.org%2fwiki%2ffile%3a2016_minn esota_state_fair_02.jpg&psig=aov Vaw1TiJs11LYrxcErXzjqhO76&ust= Waiting in lines at the state fair for better or worse is part of the experience! As more people join the line, the waiting area expands. The set of figures below describes how large the waiting area is in each stage of growth. Each block represents 1 square meter. 1. What patterns do you notice in the set of figures? 2. Is there a linear relationship between the figure number and the total number of blocks? Why or why not? Page 23

28 NC Math 1 Unit 7 Quadratic Functions 3. Sketch the next figure in the sequence. 4. Determine an equation for the total number of blocks in any figure in the sequence. Explain your equation and show how it relates to the visual diagram of the figures. Page 24

29 NC Math 1 Unit 7 Quadratic Functions 7.5 READY Topic: Finding dimensions or lengths using perfect squares. List the dimensions of each square. 1. Area = 144 in 2 2. Area = 4x # ft 2 3. Area = 36 m 2 4. Area = 49x % cm 2 List the area of square given a side length. 5. Side = 11 ft 6. Side = 13x mi 7. Side = 5 yd 8. Side = 10y in SET Topic: Quadratic patterns 9. Match the following three patterns with their equations in explicit form. I. f(n) = 3n # II. g(n) = n # + 4 III. h(n) = n # 1 Page 25

30 NC Math 1 Unit 7 Quadratic Functions 7.5 GO! Topic: Solve a literal equation for a given variable and apply the distributive property to simplify expressions Use steps for solving equations to solve each equation for x. 10. ax # + c = d 11. mx # n = p Use the distributive property to simplify each of the following expressions (2x 9) 13. 2x(5x + 6) 14. 3x # (4x 11) 15. 8x(3x # 9x) 16. 8(3x + 1) + x(2x 4) 17. 2(5x 2) + x(7x + 6) 18. x(2x 4) 3(x + 8) Page 26

31 NC Math 1 Unit 7 Quadratic Functions 7.6 Homegrown Music Fest A Solidify Understanding Task ce=images&cd=&cad=rja&uact=8&ved=2 ahukewilskzj1d3cahuqeawkhcveargqj Rx6BAgBEAU&url=http%3A%2F%2Fwww.jber.jb.mil%2FNews%2FArticles%2FArtic le%2f932122%2fgod-givenvoice%2f&psig=aovvaw0hzqakycuqwi 3IYdviHl_Z&ust= The State fair puts on a ton of concerts over the 10 days it is open. The concert promoter has hired you to help decide how much to charge for some of the tickets! If tickets for Maurice and the O s were $6, the fair would make a profit of $12,000, but they could actually make more money! If they raise their ticket prices by $1, their profit would then be $13,300. If they raise their ticket prices by $2, their profit would be $14,400! 1. If this pattern continues, how much should they raise their ticket prices to ensure they will make a maximum profit? Will there ever be a maximum profit, or will the profit continue to grow if you continue to increase the ticket price? Use multiple representations to defend your answer. 2. At a ticket price of $14 (which is raising the ticket price by $8) what is happening to the profit? What will happen to the profit at a ticket price of $15? How can you explain this? Page 27

32 NC Math 1 Unit 7 Quadratic Functions 3. Describe the pattern/relationship between the ticket price and the profit. Is there a pattern that exists with the number of people attending the concert as well? 4. If the ticket price is FREE ($0) the profit should be $0, can you use your representations to prove this theory? 5. Is there another ticket price that would result in $0 profit? How could you find this amount? How could this possible? Page 28

33 NC Math 1 Unit 7 Quadratic Functions 7.6 READY Topic: Find an expression for area Write and simplify an expression for the area of each figure below. 1. square miles 3. Area of shaded region: ft 2 (w) ft (w + 3) ft (2w) ft (3x) mi (7w 3) ft (5x + 3) mi 2. square inches 4. Area of shaded region: cm 2 (0.6x) in (5.8x) in (5x 1) in (2x + 3) in (x) cm (3x + 2) cm (5x) cm SET Topic: Using quadratic patterns to answer questions. 5. If you want to sell your cupcakes for $2 per dozen, you can make a profit of $160. If raise the cupcake price by $1, you can make a profit of $216. If you raise the cupcake price by $2 (which makes them $4 per dozen) you can make $256 profit. What is the maximum profit you can make? What should you charge for your cupcakes?

34 NC Math 1 Unit 7 Quadratic Functions Given the table below, identify the pattern. Continue the pattern to find the maximum. x y Given the table below, identify the pattern. Will there be a maximum value? How can you tell? x y Given the graph below, find the maximum as an ordered pair. (1, 13) (2, 6) (3, -3) Page 30

35 NC Math 1 Unit 7 Quadratic Functions 7.6 GO! Topic: Find the x-intercept of a linear function Find the coordinates of the x-intercept for each line. 9. (, ) x y (, ) x + 4y = 24 (, ) y = x -12 (, ) (, ) Page 31

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37 NC Math 1 Unit 7 Quadratic Functions 7.7 Circle C Racing Pigs A Solidify Understanding Task &cd=&cad=rja&uact=8&ved=2ahukewiyj- SYm9ncAhUKi6wKHcm9DqQQjRx6BAgBEAU&u rl=https%3a%2f%2fwww.flickr.com%2fphotos %2Fimagined_horizons%2F &psig=A OvVaw28gQOvu7IsbHCPfL8q3dug&ust= Dennis Cook runs the Circle C Racing Pigs on the Hogway Speedway at the N.C. State Fair. Everyone loves to watch the swift swine rush around the track to get a cheese puff, which is what they are awarded at the end of the race. Mr. Cook wants to create a pen outside of the pig trailer so that the pigs can meet and greet their fans. He will use one side of the trailer for part of the pen and has enough money for 80 feet of fencing material. 1. What are some possible dimensions for the pen? Use multiple representations to show your possibilities. 2. Would a long skinny rectangular pen have more or less area than a square pen? Explain how you know. 3. Write a function to represent the areas of this pen in terms of its width. Be sure to clearly label what each of your variables represents. Page 33

38 NC Math 1 Unit 7 Quadratic Functions 4. What is the maximum area for the pen? What are the dimensions that would give the pen the maximum area? (The pigs deserve the biggest and best!) Show this maximum using both a table and a graph. 5. What are the x-intercepts of the function? How do the x-intercepts relate to the context? 6. Describe where the table/graph is increasing and decreasing. Explain what each means in context. 7. What is the relationship between the x-intercepts and the vertex of the function? Page 34

39 NC Math 1 Unit 7 Quadratic Functions 7.7 READY Topic: Naming Conventions of Polynomials Classifying Polynomials: Write each polynomial in the correct cell below based on its name. 4x 3 4x % 2x z 5d % 7 2x % 5x + 1 5a 121 5k 5 3y % 0 15a % 21 Constant Monomial Linear Monomial Quadratic Monomial Linear Binomial Quadratic Binomial Quadratic Trinomial Write each polynomial in simplified, standard form. Then, name each polynomial. 1. 4x(x 2) Simplified, standard form: Name of polynomial: Page 35

40 NC Math 1 Unit 7 Quadratic Functions x 3 + 2x + 7 Simplified, standard form: Name of polynomial: 3. 2x(x 4) + 4x 5 Simplified, standard form: Name of polynomial: SET! Topic: Find the x-intercepts and the vertex of a quadratic function given the graph. Identify the x-intercepts and the vertex. 4. x-intercepts: 5. x-intercepts: Vertex: Vertex: x-intercepts: x-intercepts: Vertex: Vertex: Page 36

41 NC Math 1 Unit 7 Quadratic Functions If the x-intercepts of a quadratic function are (8,0) and (6, 0), what is the x-coordinate of the vertex? 9. If the x-intercepts of a quadratic function are (-4,0) and (4, 0), what is the x-coordinate of the vertex? 10. Given a vertex with an x-coordinate of 7, what are two possible x-intercepts for this quadratic? GO! Topic: Properties of Exponents Evaluate each expression ( 5 - ) Simplify each expression a a ( x ) ( 4a b) x æ4a ö ç 4 x 2b è ø 2-3x y ( ) x y x y xy x y 20x y Page 37

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43 NC Math 1 Unit 7 Quadratic Functions 7.8 Nothing Could Be Finer A Practice Understanding Task ges&cd=&cad=rja&uact=8&ved=2ahukewilo Y3Ko9ncAhUFY6wKHQRlA_sQjRx6BAgBEA U&url=https%3A%2F%2Fen.wikipedia.org%2 Fwiki%2FNorth_Carolina_State_Fair&psig=A OvVaw0zBWRTG9jxlB43SoIa2r3q&ust= Fairgoers can take home some official State Fair souvenirs from The Nest in the Expo Center lobby. This year, The Nest has a new hat design to celebrate 150 years of the State Fair and they want to decide on a price that maximizes profit. The graph below represents profit P(x) in hundreds of dollars generated by each hat price, x. 1. If The Nest wants to make a maximum profit, what should the price of the hat be? 2. What is the minimum price of a hat that produces profit for The Nest? Explain your answer. Page 39

44 NC Math 1 Unit 7 Quadratic Functions 3. Estimate the value of P(0), and explain what the value means in the context of the problem and how this may be possible. 4. If The Nest wants to make a profit of $13,700, how much should they charge per hat? 5. Find the portion of the domain that results in a profit for The Nest, and find the corresponding range of profit. 6. What hat price(s) give us an increasing profit? Decreasing profit? 7. Choose the interval where the profit is increasing the fastest: (2,3), (4,5), (5.5, 6.5), or (6,7). Explain your reasoning. 8. The Nest owner believes that selling the hat at a higher price results in a greater profit. Explain to the owner how selling the hat at a higher price affects the profit. Page 40

45 NC Math 1 Unit 7 Quadratic Functions Part 2: Match each quadratic to the appropriate graph. 1. y = (x 2)(x + 4) 4. y = (x 1)(x + 3) 2. y = (x 2)(x + 2) 5. y = (x + 1)(x 3) 3. y = 2(x 2)(x + 1) 6. y = (x 2)(x + 3) A B C D E F Identify which key features were helpful in matching these equations with their graphs. Given this pattern, could you write a possible equation to match the profit graph P(x) above? Page 41

46 NC Math 1 Unit 7 Quadratic functions 7.8 READY Topic: Key Features from a Quadratic. 1. Define the following characteristics of the quadratic function f(x) = x 2 4x Vertex: Minimum or Maximum? Axis of symmetry: X-intercepts: Y-intercept: Increasing: Decreasing: Domain: Range: 2. Define the following characteristics of the quadratic function y = x 2 4x 5 Vertex: Minimum or Maximum? Axis of symmetry: X-intercepts: Y-intercept: Increasing: Decreasing: 6 3 Domain: Range: Page 42

47 NC Math 1 Unit 7 Quadratic functions 7.8 SET Topic: Use key features to interpret a quadratic in context. Consider the graph of the quadratic function shown below and answer the questions. A company is comparing their toy price (x) and their profits(y). Use the graph to help answer the following questions. 3. If the company wants to maximize profit, how much should the toy cost? Profit 4. What is the minimum price a toy should cost to make any profit? 5. If the company wants to make a profit of $400, how much should the toy be sold? Toy Price 6. Find the domain and range that result in a profit for the company. Page 43

48 NC Math 1 Unit 7 Quadratic functions 7.8 GO! Topic: Solve a system of equations Solve the following system of equations. 7. y = 3 x 5x + 3y = x 3y = 8 3x 7y = 7 9. The perimeter of a rectangular wooden deck is 90 feet. The deck's length, l, is 5 feet less than 4 times its width, w. Which system of linear equations can be used to determine the dimensions, in feet, of the wooden deck? 10. A movie theater charges $5 for an adult s ticket and $2 for a child s ticket. One Saturday, the theater sold 785 tickets for $3280. How many of each type of ticket were sold? Page 44