Quadratic equations Questions and Answers

Alain throws a stone off a bridge into a river below The stone s height in meters above the water a seconds after Alain threw it is modeled by h x 5x 10x 15 What is the height of the stone at the time it is thrown meters

For the polynomial function f x 6 x 1 x 3 answer the following questions a List each real zero and its multiplicity b Determine whether the graph crosses or touches the x axis at each x intercept c Determine the maximum number of turning points on the graph d Determine the end behavior that is find the power function that the graph of f resembles for large values of x HH SIVULLUIS SI Type integers or fractions OC The smallest zero of fis zero of f is with multiplicity Type integers or fractions D There are no real zeros puny myuvILVIV SITE with multiplicity The middle zero of f is www pmny with multiplicity b Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The graph crosses the x axis at Type an integer or a simplified fraction Use a comma to separate answers as needed The largest OB The graph touches the x axis at Type an integer or a simplified fraction Use a comma to separate answers as needed and crosses at OC The graph touches the x axis at Type integers or simplified fractions Use a comma to separate answers as needed The graph neither crosses nor touches the x axis

The graph of below is complete since it displays all roots the end behavior and the y intercept of the graph of f Use the graph of f to answer the following questions Note all and y intercepts are integer values 3 2 5 4 27 1 1 2 5 6 1 2 List all roots with even multiplicity If more than one such root exists use a comma separated list to optor the roots

4 Admission 5 00 Apples 0 75 per lb a Which equation represents the cost in dollars of going to the festival and picking a pounds of apples O y 5x 0 75 The cost of going to the festival is the sum of the cost of picking pounds of apples b Graph the equation you chose in part a Line 15 Undo Redo x Resel y 0 75x 5 and the cost of admission 5

h z 3r 18r 12z 72 Use the Leading Coefficient Test to determine the end behavior of the graph of h Determine the roots of h and the multiplicity of each root Also describe the behavior of the graph at each root If a third root does not exist enter DNE when appropriate According to the Leading Coeffiecient Test the graph of h O falls to the left and rises to the right O rises to the left and falls to the right O falls the left and falls to the right O rises to the left and rises to the right Determine the roots of h Enter solutions using a comma separated list The multiplicity of the least root I The multiplicity of the greatest root The multiplicity of the other root I is 11 is is

Write an equation of the form y acos b x c with the given amplitude period and phase shift Amplitude Period Phase shift R13 35 1 15 The equation of the form y acos b x c is Tyne an exact answer using as needed Tyne an equation

Use a system of equations to find the partial fraction decomposition of the rational expression Solve the system using matrices 4x 3x 3 x 1 x 1 A BM A x 1 B x 1 C x 1

2 At Mumford High School the robotics team is holding a bake sale to help raise money for materials to build a new robot They use 35 of the money to pay back their members for the cost of baking the food and the rest of the money is kept by the team to build the robot If they sell 500 in baked goods how much money will the team keep to build the robot A 35 B 65 C 175 D 325

Consider the following function g x 1125 z 6 6 Determine the IT intercepts of g and the multiplicity of each intercept Also describe the behavior of the graph at each Z intercept The multiplicity of the least root z The multiplicity of the greatest root I The multiplicity of the other root I At the least root I At the greatest root I At the other root I 1 1 is J J is is the graph of g Select an answer the graph of g Select an answer the graph of g Select an answer

Consider the following function f x 15 z 14 x 12 Determine the zeros of f and the multiplicity of each zero Also describe the behavior of the graph at each zero The multiplicity of the lesser root x The multiplicity of the greater root At the lesser root a At the greater root is is the graph of f Select an answer the graph of f Select an answer

3 In a bag there are 8 green marbles 12 blue marbles and 5 red marbles What percentage of the marbles in the bag is red or green

15 Brad is a wrestler trying to make weight He currently weighs 184 pounds If he cuts 2 pounds per week how many weeks will it take him to weigh no more than 165 pounds Write an inequality to represent this situation use w for the number of weeks Type a response 16 The cheerleaders are selling tickets to the spaghetti dinner They need to raise at least 900 The tickets cost 5 each Write an inequality to represent how many tickets they need to sell to meet their goal use t for the number of tickets sold Tyne a response

5 Simplify 3 48 6 108 6 Multiply Give your answer in radical form 11 2 13 7 Simplify Give your answer in radical form 2 125

Simplify 9 56x7y 2 Assume x and y are nonnegative 12 O 18x y6 14x O 2x y6 14x O 18x y6 14

Multiply 3 7 17 Enter your answer in radical form in the box Basic 7 Y DO 1

What is the expression in radical form 7x y Enter your answer in simplest form in the box

Simplify 8 200 3 162 Enter your answer in simplest radical form in the b

Simplify 3 6 15 O 3 2 9 5 O 3 2 3 5 O 3 7 O 2 3 3 5

Simplify 7i 75 Enter your answer in simplest radical form in

1 Complete the table below REMEMBER These problems are testing your skills and understanding of RADICALS not if you can use a calculator Each completely correct line is worth 3 points If you simplify be sure to use the rules and conventions you learned in Unit 2 Expression 5 3 8 3 5 2x 3y 2 x4y Can it be simplified OYES NO OYES NO YES NO OYES NO YES NO If NO explain why not If YES simplify completely and rewrite in the most simplified radical expression SHOW ALL WORKI

3 6 A MATCH THE LETTER UNER SACH SYMBOTH THE CORRECT WORDING GREATER THAN 2 3 4 5 6 D LESS THAN AT MOST AT LEAST NO MORE THAN NO LESS THAN O

8 Translate the verbal phrase into an inequality use x as your variable Don t solve 5 more than the product of 2 and x Type a response D 9 Translate the verbal phrase into an inequality use x as your variable Don t solve The sum of x and 1 is at least 9 Type a response U

7 Translate the verbal phrase into an inequality use x as your variable Don t solve The difference of x and 7 is less than 4 Type a response it may be difficult to format the and symbols so use the following FOR TYPE or press ALT and TYPE 755 then release ALT

Charlie attempted to find the value of expression 3 4 2 8 His work is shown below e ame 3 4 2 8 12 2 8 10 8 100 8 4 108 Complete the follow ing tasks Explain the error Charlie made when evaluating the expression State what Charlie s answer should have been

st all potential rational zeros x 5 3x 2 Which of the following choices lists all the potential r OA 0 1 2 OB 1 O C 1 2 OD 2

1 For the function f x x 3 use the leading term test and the knowledge of y intercepts to match the function with one of the graphs below Choose the correct answer below OA Q O B Q O C Q G OD

4x 3 10 4x 14 what is the value of x Justify your response by showing your work e the sketchpad below to show your work and justify your response a O PENCIL THIN BLACK 2 4x 3 10 4x 14

A linear function g models a relationship in which the dependent variable increases 2 units for every 1 unit the independent variable increases Graph g when g 0 4 Identify the slope y intercept and x intercept of the graph Line Move Undo 5 4 3 2 1 5 4 3 2 19 2 3 4 5 Redo 1 2 3 x Reset 4 5

IN IDEAS MATH Eten Identity the graph of g x O 41 O A Ay 9 14 O O 2 Ay 50 HE tx Jett Doucet B Assignment Player Save Exit dy dubmit Choose the description of the transformation from the graph of x x to the graph of g O The graph of g is a vertical stretch of the graph of by a factor of 3 O The graph of g is a vertical shrink of the graph off by a factor of O The graph of g is a vertical stretch of the graph of by a factor of 3 and a reflection in the x axis Choose the description of the domain and range The graph of g is a vertical shrink of the graph off by a factor of and a reflection in the x axis O The domain is all real numbers The range is y 0 O The domain is all real numbers The range is y 20 O The domain is x 20 The range is all real numbers O The domain is all real numbers The range is the all real numbers

Listen Let f x 2x 2 Graph g x f x 3 Line Move Undo 8 Previous 6 4 2 8 6 4 29 4 6 8 1 2 Redo 4 6 8 2 3 x Reset 4 5 6 Next Choose the description of the transformation from the graph off to the graph of g The graph of g is a vertical translation 3 units up of the graph of f The graph of g is a vertical translation 3 units down of the graph of f The graph of g is a horizontal translation 3 units left of the graph of f The graph of g is a horizontal translation 3 units right of the graph of f

Estimate the intercepts of the graph of the function 4 6 4 2 y y x x 2 2 The x intercepts are about 4 x and and the y intercept is about

Nick has 50 He just got a job as a construction worker making 10 an hour He wants to earn enough money to buy himself a new cell phone val at 900 How many hours must he work to buy the phone Write an inequality x Nick must work at least hours

e C D at in 5 t 49 y 8 u 8 9

Given the inequality 6 1 2r 26 2r 1 2x which of the following are included in the solution Select all that apply A 2 B C 4 5 D 1 G

Given the function f x 3 x 2 5 Compared to the parent function this function has been horizontally translated by this function has been vertically translated by the function is the function is reflected over the l units to the units by a factor of

Simplify the complex rational expression by using either method Be sure to remove any common factors 8 p 5p 24 6 12 P 3 P 8

Simplify the complex rational expression by using the LCD Be sure to remove any common factors 2 w 7 W 8 9w w 56

Simplify the complex rational expression by writing it as division Be sure to remove any common factors 12w w 6 w9 w 36

10 If Taylor does her homework 75 of the time how many homework assignments did she complete if there were 60 assignments given one semester

12 In a semester of math class there are a total of 600 points that can be earned In order to eam a grade of 80 or higher how many points would a student need to earn

11 Deja collects baseball cards Her favorite team is the Chicago Cubs 20 of her cards are Cubs players If she has 50 baseball cards of players on the Cubs how many cards are in her collection DERUES JOGFELET

1 vertex form of a quadratic function lesson qui

8 Simplify completely b 125 3 a 25 2 333 c 64 3 d 49 2 0 e 8 1 27 f

6 Write in radical form and simplify 3 a 252 5 b 162 c 27 33 2 d 1253 e 49 N W F 125 f 64

4 Write in exponential form a 7 b 10 10 4 915 c 228 d 157 48 e 115 f V101

Verify the identity tan 0 cot 0 sec 0 csc 0 Use a Reciprocal Identity to rewrite the expression in terms of sine and cosine as a single rational expression tan 0 cot 0 sin 0 cos 8 cos 0 sin 0 sin 0 Use a Pythagorean Identity to rewrite the expression in terms of a single function and then simplify cos 8 sin 0

7 In a baseball game Chris gets a hit 2 times takes a walk once strikes out once and grounds out once In what percentage of his at bats did he get a hit

For the polynomial function f x 5 x 1 x 3 answer the following questions a List each real zero and its multiplicity b Determine whether the graph crosses or touches the x axis at each x intercept c Determine the maximum number of turning points on the graph d Determine the end behavior that is find the power function that the graph of f resembles for large values of x Type integers or iacuons OD There are no real zeros b Select the correct choice below and if necessary fill in the answer box es to complete your choice A The graph touches the x axis at Type an integer or a simplified fraction Use a comma to separate answers as needed B The graph crosses the x axis at 3 Type an integer or a simplified fraction Use a comma to separate answers as needed OC The graph touches the x axis at and crosses at Type integers or simplified fractions Use a comma to separate answers as needed D The graph neither crosses nor touches the x axis c The maximum number of turning points on the graph is 6 Type a whole number d The power function that the graph of f resembles for large values of x is y

2 Kayla records the weather for several days in a row There are 10 suppy days 8 rainy days

2 Peter got 80 on a science test If he answered 12 questions right how many were there overall