Quadratic equations Questions and Answers

6 Find a number halfway between and 1 4 16 x

2 70 292 972 30 52 Q 292 970 30 133 33

14 Express the following decimal as a fraction 0 6666

15 If x is an integer in the set of real numbers as x increases what happens to the expression

6 What is the scale factor if a 12 in by 8 in photograph is enlarged to a poster that is 3 ft by 2 ft 4 O 1 10 01 1 12 13

2 What is the scale factor if a 4 by 10 photograph is enlarged to a poster that is 2 ft by 5 ft

alculate the distance between the points H 3 2 and L 2 1 in the coordinate plane ve an exact answer not a decimal approximation 10 8 6 H 4 10 8 44 2 4 6 8 10 Distance 010

6 How much water should be added to 30 ml of 65 percent acid solution to dilute it to a 55 percent acid solution ml

14 Solve 3x 4x 3 x 2 0 Identify all the correct solutions roots More than one answer may be correct select all that apply c 2 0x x 0 0 x x 10 x 16 0x 1

10 The local recreation center has asked you to design a machine that launches a hopper full of basketballs at a hoop so the team can practice rebounding drills The machine needs to adjust to multiple hoop heights for all age levels The equation that represents the height of the basketball as a function of time t in seconds is h 16t 27 2t 3 How many seconds does it take for the ball to reach a hoop 7 high More than one answer may be correct select all that apply Ot 1 67 seconds Ot 1 54 seconds Ot 1 48 seconds Ot 0 10 seconds Ot 0 16 seconds Ot 0 29 seconds None of these is correct the ball never reaches 7 feet

Situation 2 You are the coach of the soccer team To start practice you want the players to do some running on the field The players have two options They can run from end to end the red line or they can do the diagonal the blue line Experiment with different heights and widths for your field 2 Refer to situation 2 You are doing a series of runs and want to emphasize distance Your first option is to run 6 diagonal runs Your second option is to run 7 field runs Which option will give you the greatest distance If you want the field runs to be greater than the diagonal runs what length and width would be necessary for

9 A pumpkin is fired upward with an initial speed of 800 feet per second It is given that h 13t 650t his the height of the pumpkin at any given time Use your graphing calculator to find how many seconds before the pumpkin hits the ground Or factor and solve for t algebraically Ot 50 seconds O t 4 seconds Ot 8 seconds O t 13 seconds Ot 0 seconds

13 Identify the range of the following equation y x 14 43 Oy 6 Ox 3 Oy 11 O x 27 0 23 x 7 O all real numbers

2 Choose one of these polynomial functions then answer the questions below using that equation A f x 2x 8x 22x 60 B f x 3x 6x 15x 18 In the answer box share your process to factor the polynomial function completely Be sure to share some strategies you use to f

4 In your opinion which is the best and simplest way to factor polynomials including quadratics Explain why you chose this method compared to other methods there some exceptions to this maybe a polynomial that might factor better with another method

In this activity you will be asked to answer questions using some of these polynomial equations f x x 9x 8x f x 2x 8x 22x 60 15x 18 f x 3x 6x f x 2x 4x 30x 1 Choose one of these polynomial functions then factor it completely A f x x 9x 8x B f x 2x 4x 30x In the answer box share your process to factor the polynomial function Be sure to share some strategies you use to fa

5 Find the inverse equations for fand g f x 3x 5 g x x 6 Explain your process Then write about the relationship between the functions and their inverses Does the domain and range of all functions and inverses follow

6 Determine whether the pair of functions are inverse functions f x 2x 1 g x 2x 1 O yes O no

7 Find the inverse of the function Mark all correct answers f x 3x 7 0 2 7 3 7 0 7 0 0 7

12 Determine whether the pair of functions are inverses of each other f x 6x 9 g x 9 O no O not enough information O yes

Find an equation for the line below C5 4 5 1

5 Find the inverse of the function f x 9x 4 O 0 2 1 4 9 0 4 O 4

below 2 B 3 C 2 Find the values of the six trigonometric functions using a calculator if 0 26 Round answers to the nearest thousandth 3 Solve tan 0 89 325 Round your answer to the nearest degree

7 To wrap an expensive gift you ll need a box Graph the following equation 12 2x 19 2x x which represents of the volume of a box made from a rectangular cardboard sheet 12 inches wide and 19 inches long from which a square is cut from each corner and the sides of the box are folded as shown The value a represents the side length of the square cutout What is the length x of a side of the square cut from each corner of the paper used to find the maximum volume for V 12 2x 19 2x x Round your answer to the nearest hundredth

13 You ve been asked to program the flight of a chicken shot out of a cannon over a barnyard wall for a new animated feature film You estimate the bird needs to clear at least 9 feet in order to sail over the wall The equation that represents the height of the chicken as a function of time t in seconds is h 16t 68 8t What is the realistic domain for this scenario Ot positive real numbers from 0 to 4 3 Oh positive real numbers O h all real numbers Oh positive real numbers from 0 to 73 96 O t all real numbers Ot positive real numbers

What is the end behavior of the graph of the polynomial function f x 2x 26x As x co and as xo co As x co co and as xo co As x co Y co and as xco As x co Yo and as xco co co

13 You want to rent a surfboard for some surfing The rental company employee says it s a flat fee of 73 to rent the surfboard and an additional 25 per hour used Also you may only keep the surfboard for a maximum of 38 hours What is the domain of the function O all real numbers O all real numbers between 0 and 38 O all real numbers between 25 and 1023 O positive real numbers

15 The local recreation center has asked you to design a machine that launches a hopper full of basketballs at a hoop so the team can practice rebounding drills The machine needs to adjust to multiple hoop heights for all age levels The equation that represents the height of the basketball as a function of time t in seconds is h 16t 32t 3 How many seconds does it take for the ball to pass through a 8 foot hoop coming down Round to the nearest hundredth ball passes through the hoop at t seconds

Suppose that the functions f and g are defined for all real numbers x as follows f x x 4 O g x 3x Write the expressions for f g x and f g x and evaluate f g 3 f g x f g x f g 3 X G

4 To store some important papers you ll need a box Graph the following equation 10 2x 19 2x x which represents of the volume of a box made from a rectangular cardboard sheet 10 inches wide and 19 inches long from which a square is cut from each corner and the sides of the box are folded as shown The value a represents the side length of the square cutout Use the graph to find the maximum volume of the box maximum volume cubic inches

6 The police department uses a formula to determine the speed at which a car was going when the driver applied the brakes by measuring the distance of the skid marks The equation d 0 0018r models the distance d in feet traveled after applying the brakes in a car moving r miles per hour r is the speed of the car How long will the skid marks be if the car is traveling 64 52 mph Round your answer to the nearest hundredth of a foot length of skid feet

depar speed at which a car was going when the driver applied the brakes by measuring the distance of the skid marks The equation d 0 05r r models the distance d in feet traveled after applying the brakes in a car moving r miles per hour r is the speed of the car Using the stopping distance formula above and the graph below what point on the graph allows you to find the speed that the car may travel if it needs at least 25 feet to come to a complete stop 32 25 y 05x x O Point B 60 40 20 y 45 40 35 30 25 20 15 10 5 B X

2 Your math teacher holds a contest where teams launch water balloons at each other s targets The balloon launchers are math based so you must enter quadratic functions to aim your launcher Your teammate has determined the following equation will launch a balloon at the other team s target h 16t 94t 5 where t represents the time in seconds after the balloon s release and h represents the height of the balloon The height versus time graph for the equation looks like this What is a reasonable domain for this situation Hint Set 0 equal to 16t 94t 5 and solve for t using the quadratic formula Check your answer on a graphing calculator 00 t 5 928 00 t 4 6

Solve for x 645x 9 2x 25x 50 If there is more than one solution separate them with commas X 0 8

10 4 Demand D as a function of price P is given by D P See Problem 4 2 7 for a economic interpretation Solve the equation for P and find the inverse demand function

5 Graph the following using a graphing calculator Identify all of the roots of the equation 9x 10 More than one answer may be correct select all correct answers 1 05 1 96 x 0 60 x 1 96 0 60 22 1 05 There are no real roots

3 Graph the following using a graphing calculator State how many zeros roots the equation has 8x 1 number of roots

2 Graph the following using a graphing calculator State how many zeros roots the equation has 6x 4x 100x 75 number of roots

An aircraft factory manufactures airplane engines The unit cost C the cost in dollars to make each airplane engine depends on the number of engines made Ifx engines are made then the unit cost is given by the function C x 0 7x 280x 39 681 How many engines must be made to minimize the unit cost Do not round your answer Number of

You deposit 500 each month into an account earning 7 interest compounded monthly a How much will you have in the account in 30 years b How much total money will you put into the account c How much total interest will you earn

number of members of the Athletic Booster Club during various years Athletic Booster Club Number of People 80 70 60 50 40 30 20 10 0 2012 2013 2014 2015 2016 Year 100 In which year was the membership 40 greater than it was in 2012 H 2015 J 2016 F 2013 G 2014

onsider the following function q x Answer x 3 Step 2 of 2 Determine the domain and range of the original function Express your answer in interval notation Domain 5 U 3 00 5 Range 0 5 I

0 52 14z and the reverb is more than or equal to this expression 2z 96 where z represents the number of instruments in the mix These expressions can be written as inequalities ys 0 52 14z y2 2 96 Here s a graph of these two inequalities 80 401 15 30 X a Explain what steps you would take to find the points of intersection of the two curves on the graph b Determine which of the following points lie in the optimal range 8 80 16 100 22 80 20 80 16 60 19 5 73 6 c How do you know which of these points is in the optimal range when you use the graph d How would you prove which of these points are in the

James invests 5 000 at 10 simple interest for 6 year How much is in the account at the end of the 6 years period Answer S

1 Stainless steel is an alloy mixture of metals that many forks knives and spoons are made of To make the stainless steel a company mixes 4 5 pounds of chromium and 2 pounds of nickel with 18 5 pounds of iron a A regular spoon weighs about 25 grams Explain how you could find out what percentage of the spoon s weight is due to chromium How much is this in grams b A pound of iron costs 32 while a pound of nickel is 8 per pound Chromium costs 145 per pound How much does it cost the company to make 60 pounds of stainless steel Explain your thinking

Situation 2 Soccer Treats Diego s high school soccer team started a fundraiser selling treats at their games They spent 1000 to start and an additional 0 30 on each candy bar and can of soda They decide to sell both the candy and the soda for the same price to make things simple Choose a reasonable price for the team to sell the candy bars and sodas In your discussion post share the equations that you used to model this situation and answer the following questions remember that profit is the revenue minus the costs 1 How much do they need to sell to break even where revenue is equal to cost 2 How much do they need to sell to make at least 5 000 in profit 3 Do you think it is likely for them to make at least 5 000 in profit In what situations would it be possible for them to make at least 5 000 in

You are starting a sock company You must determine you costs to manufacture your product The start up cost is 2000 which helps you purchase sew machines Material and labor is 2 50 per pair of socks a Write an equation to model your company s cost for manufacturing the socks i e y mx b D Which variable represents the domain Explain your ans c What is the domain for this situation d Which variable represents the range Explain your answ e What is the range for this situation F Using your equation what would be the cost of manufacturing 25 pairs of socks g How many socks could you make with 2500 Create a coordinate graph on a sheet of paper to represe this situation Describe the graph Include the dimensions

1 How many lines do you think could pass through the y intercept 4 What makes each line special

3 Find the equation of a line passing through points 7 10 5 14 y

5 In the graph below an equation of line J is y x y HH y x X