Quadratic equations Questions and Answers

e graph of a polynomial function is given What is the smallest degree that the polynomial could have

The graph of a polynomial function is given What is the smallest degree that the polynomial could have

Use the simplex method to find the optimal solution Assume all variables are nonnegati Minimize f 3x 2y subject to the following constraints x y 15 x y 2 25 x y 35 f

Fill in the blank to correctly complete the following sentence The graph of f x x is a reflection of the graph of y x across the x axis

Use the graph below of a function to find all integer values of x for which f x 4 Separate multiple answers with a comma 6 MN 2 1 2 4 6 46 Enable Zoom Pan 8 6

The plot below represents the function f z 10 9 8 7 6 34 Find the indicated values a f 1 b if f 2 4 then z A Ra 10 9 for the tavs6 S 2 7593992 6 7 NE 9 10 to 5 6 7 8 9 10

Find a polynomial of the specified degree that satisfies the given conditions Degree 4 zeros 1 1 6 integer coefficients and constant term 18 30x319x 30x 18 f x 4 X

actor the polynomial and use the factored form to find the zeros Enter your answers as a comma separated list Enter all answers including repeti P x x5 9x3 X ketch the graph 3 2 y 3 2 1 40 20 20 40 y 40 20 20 1 2 40 X O 2 1 y 20 10 20 10 NAV X 2 3 2 1 10 10 20 y 1 2 20 1 2 3 X X

Terry is skiing down a steep hill Terry s elevation E t in feet after t seconds is given by the equation E t 2200 40t Complete the following sentence describing Terry s starting elevation and how it is changing over time He is starting from a height of feet and is skiing downhill at a speed of numbers Note to get the problem correct you must provide the correct answer to every part per E

Graph the line that passes through the point 4 5 with a slope of Give an equation for this line What is the y intercept for this line Y use exact numbers no decimals give your answer as a point use exact numbers no decimal

Fernando is walking home from a friend s house at a constant speed After 4 minutes he is 2 miles from home 14 minutes after leaving he is 1 2 miles from home What is his rate in miles per hour mph mph help numbers

Find a linear equation satisfying the following f 1 13 and 5 41 f x help formulas

Question 1 of 20 What is the value of the y coordinate of the y intercept of the function shown below x 3x 5x 4

Sales of SUVS sport utility vehicles in the United States in millions for the years 1990 1999 can be modeled by the quadratic equation shown below y 0 016x 0 124x 0 787 Here x 0 represents 1990 x 1 represents 1991 and so on Use the model to approximate sales in 1998 Sales in 1998 were approximately million SUVS Round to the nearest tenth as needed

Question 2 of 10 The equation for a projectile s height versus time is h t 16t Vot h A tennis ball machine serves a ball vertically into the air from a height of 2 feet with an initial speed of 130 feet per second Which equation correctly models the ball s height as a function of time A h t 16t 2t 130 h t 16t 130t 2 c h t 16t 2t 130 D h t 16t 130t 2 OB SUBMIT

Only one of the equations is set up so that the values of a b and c can be determined immediately Which one is it Solve it Choose the correct equation below which is set up such that the values of a b and c can be determined immediately OA 5x 34x 7 0 OB 3x 4 7 OC x x 2 D 5x 1 x 1 0

f x 7x 3 p x 2x x 7 0 quotient remainder Need Help Submit Answer P x m r p m x iven p x sing interval notation 12 Read It X Watch It 1 and m x x 1 state the domain of each of

Using the graph to the right if f x 0 determine the values of x Select all that apply A 4 B 1 C 2 D 8 E O GELEE 10 B B 6 421 4 20 B 10 Q Q G

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Solve for x x 16 x 4 O no solution O x 9 O x 8 O x 0 or x 9

Solve for x 8x 9 x 3 O x 0 or x 2 O x 0 or x 2 O x 2 or x 3 O x 3 or x 2

Solve for b a b c 3 O b 9 a c O b 9 a c O b 3 a c O b 3 a c

Find the amplitude the period any vertical translation and any phase shift of the graph of the following function y 6 sin x What is the amplitude of the function 1 Type an integer or a simplified fraction What is the period of the function C T Simplify your answer Type an exact answer using x as needed Use integers or fractions for any numbers in the expression What is the vertical translation of the function Select the correct choice below and fill in any answer boxes within your choice A The vertical translation is 6 unit s Type an exact answer using x as needed Use integers or fractions for any numbers in the expression B There is no vertical translation What is the phase shift of the function Select the correct choice below and fill in any answer boxes within your choice A The phase shift is unit s to the left Type an exact answer using as needed Use integers or fractions for any numbers in the expression OB There is no phase shift

Find the amplitude the period any vertical translation and any phase shift of the graph of the following function T 5 y 6 sin 2x What is the amplitude of the function 1 Type an integer or a simplified fraction What is the period of the function 7 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression

Which rational function has the given graph O A 2x R x 2 of the X 9 O C 2x R x 2 x 9 LN O B O D R x Eco 2x 2 X R x Q 37 2x 2 X 9

Melissa plants pink and orange flowers along the driveway to her house She plants these flowers in a ratio of 3 pink to 1 orange If she plants a total of 48 flowers how many pink flowers does she plant O 16 pink flowers O 144 pink flowers O 36 pink flowers O 12 pink flowers

An electronics store sells DVD players and cordless telephones The store makes a 75 profit on the sale of each DVD player d and a 30 profit on the sale of each cordless telephone c The store wants to make a profit of at least 255 00 from its sales of DVD players and cordless phones Which inequality describes this situation a 75d 30c 255 b 75d 30cs 255 c 75d 30c 255 d 75d 30c2255

6 Ryan is a wrestler trying to make weight He currently weighs 200 lbs If he cuts 2 lbs per week weeks will it take him to weigh less than 175 lbs 7 7 Tom is deciding whether or not he should become a member gym to use their basketball courts The membership cost is 135 Members pay 2 to rent out the basketball courts Non members can rent the court also but they have to pay 11 each time how many times would Tom need to rent the court in orde for it be cheaper to be a member than a non member 8 Solve each inequality and graph its solution 8 24 6k 6 4 k 4 9 10 11 12 13 14 15 16 17 18 19 010 4 4 7x x 6x 5 4 3 2 1 0 1 2 5 6 9 11 9 2n 40 5 6 n 7n 7 6 5 4 3 2 11 7 4 x 42 18 7x 10 8 6 0 1 4 2 0

decided to reduce heat costs by installing new storm windows and adding insulation Anthony s parents offered him 10 for every storm window he installs and they owe him 25 for spreading the insulation He wants to earn more than 200 Write and solve an inequality to find out how many windows he must install Click on show your work to type or write ir work V

Write and solve an inequality that represents how many 20 bills you can withdraw from the account without going below the minimum balance Click on show your work to type or write your work You can withdraw 20 bills enter number only Your current balance is 320 00 The minimum balance is 100 00 Would you like to make another transaction

1 You can order discount movie tickets from a web site for 7 each You must also pay a service fee of 4 You want to spend no more than 40 on movie tickets Write and solve an inequality to find the greatest number of movie tickets that you can order Click on show your work to type or write your work The greatest number of movie tickets she can order is enter number only Type a response

Mrs Smith wrote Eight less than three times a number is greater than fifteen on the board If x represents the number which inequality is a correct translation of this statement a b 3x 8 15 3x 8 15 C 8 3x 15 d 8 3x 15

Students in a ninth grade class measured their heights h in centimeters The height of the shortest student was 155 cm and the height of the tallest student was 190 cm Which inequality represents the range of heights a 155 h 190 b 155 h 190 h 2 155 or hs 190 d h 155 or h 190

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Determine the amplitude period any vertical translation and any phase shift of the given graph y 3 sin x The amplitude is CI

Graph the following function 1 y c OA 1 Which transformations are needed to graph the function y 4 correct answer below OB I 12 COS T 3 The graph of y cos x should be horizontally shifted to the left by OC K shrunk by a factor of 1 4 and vertically stretched by a factor of 4 D T The graph of y cos x should be horizontally shifted to the left by 3 stretched by a factor of 4 and vertically shrunk by a factor of 12 1 shrunk by a factor of and vertically stretched by a factor of 4 4 T The graph of y cos x should be horizontally shifted to the right by units horizontally Choose the units horizontally units horizontally The graph of y cos x should be horizontally shifted to the right by 3 of and vertically shrunk by a factor of units horizontally

Fill in the blanks to correctly complete the sentence below The graph of y 3 5 sin x is obtained by shifting the graph of y 5 sin x unit s

2 1 0 0 3 2 1 0 0 T X 2x X 2x y sin x Q T 3 la 2r A 0 T 2 3 3 5x 3 51 3 Drag each graph above to match the function below x 3 y sin x TC 3 1 hinihik 0 X 1 2x 1 2 Ay 1 0 1 70 3 4x 2n X 7 3 y cos x I 3 Y 2 cos X AY 3 2 1 0 0 TC y cos x TC 3 y 2 cos x 3 41 3 3 1 2 3

The function graphed to the right is of the form y c cos x y c sin x y cos x d or y sin x d where d is the least possible positive value Determine the equation of the graph C y Type an expression using x as the variable 2 1 1 Q

Graph the following function T y sin x 6 Use the graphing tool to graph the function Click to enlarge graph For any answer boxes shown with the grapher type an exact answer Type the word pi to insert the symbol as needed C 2

Fill in the blanks to correctly complete the sentence below The graph of y 2 6 cos x is obtained by shifting the graph of y 6 cos x unit s

Determine the vertical asymptote s of the function If none exists state that fact x 2 x3 8x 12x f x Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The function has three vertical asymptotes The leftmost asymptote is Type equations OB The function has one vertical asymptote Type an equation OC The function has two vertical asymptotes The leftmost asymptote is Type equations OD The function has no vertical asymptotes the middle asymptote is and the rightmost asymptote is and the rightmost asymptote is

following function over a two period interval Give the period and the amplitude y sin 4x What is the period of the function y sin 4x 2 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression What is the amplitude of the function y sin 4x 1 Type an integer or a simplified fraction Which of the following is the correct graph of the function y sin 4x O A 8 8t OB 8 Ay 2 A X 8k O C A O D LEI G

1 a Use the fundamental theorem of algebra to determine the number of roots for 2x 4x 7 b What are the roots of 2x 4x 7 Show your work Answer

Find the following tan tan 0 N 8 given sin e 12 13 180 0 270 ACCO

Which of the following number lines depicts the solution to x 5 x 8 0 a Ob O c d 1 2 3 1 2 3 1 2 3 4 5 45 4 4 5 6 6 45 5 6 7 8 9 10 7 8 9 7 8 10 9 10 R R R

4 For the function H x x 2 a graph the rational function using transformations b use the final graph to find the domain and range and c use the final graph to list any vertical horizontal or oblique asymptotes G b What is the domain of the given function Select the correct choice below and if necessary fill in the answer box to complete your choice OA The domain of the given function is xlx is a real number x Type an integer or a simplified fraction OB The domain of the given function is xlx is a real number x Type an integer or a simplified fraction OC The domain of the given function is xlx is a real number x Type an integer or a simplified fraction Use a comma to separate answers as needed OD The domain of the given function is the set of all real numbers

2 a List the possible rational zeros of the polynomial f x 2x 3x 2x 3 b Find the zeros off

Solve this system of equations 2x 4y 20 x 4

Find the vertical horizontal and oblique asymptotes if any of the given rational function 3 x 27 R x 2 x 7x 12 www y Simplify your answer Use a comma to separate answers as needed B There is no horizontal asymptote Find the oblique asymptote s if any of the function Select the correct choice below and fill in ar within your choice A The oblique asymptote s is are y Simplify your answer Use a comma to separate answers as needed OB There is no oblique asymptote