Quadratic equations Questions and Answers

Part 1 of 2 Use synthetic division and the factor theorem to determine whether x 4 is a factor of f x f x 3x3 15x2 16x 16 Complete the first row of the synthetic division table

For the given polynomial P x and the given c use the remainder theorem to find P c P x 3x 5x 7x 3 5 P c Simplify your answer www

4 12 y x 1 3 V 3 432 2

10 y 2x 2 y2 x 3 4 3 2 1 ZO

4 2x y 3 4x y 3 A B D 4 AV H A V x X x N

7 y x 3 7 y x 3 2 A B O D

Graph linear Inequalities Sketch the solution to each system of inequalities 1 y x 3 y 3x 1 A B D 4 14 V X x 2 3 2 y x 1 2 y2 2 A B D x 1 y y y X X X x

Find the median for the data items in the given frequency distribution Score x 3 Frequency f 3 1 3 2 3 The median is Type an integer or a decimal 4 3 10 5 7 6 5 7 7 8 5 9 3 10 5

Determine whether the following statement makes sense or does not make sense and explain your reasoning Improperly worded questions can steer respondents towards answers that are not their own Choose the correct answer below GILB OA The statement does not make sense because the wording of a question does not affect how a respondent will answer OB The statement makes sense because if a question is worded improperly respondents might not know what is actually being asked C The statement does not make sense because questions cannot be worded improperly OD The statement makes sense because improperly worded questions cannot be answered correctly

The histogram shows the starting salaries rounded to the nearest thousand dollars for college graduates based on a random sample of recent graduates Determine whether the following statement is true or false according to the graph The percentage of starting salaries falling above those shown by any rectangular bar is equal to the percentage of starting salaries falling below the bar Choose the correct answer below BOCCO of Graduates Frequency 400 300 200 100 0 A False because this is not true for any rectangular bar OB True because this is true when there is odd number of bars OC False because this is only true if there is an even number of bars D True because the percentage of starting salaries falling below and above each bar must sum to 100 Starting Salaries of Recent College Graduates 41 45 46 50 51 55 56 60 61 65 66 70 71 75 Salary thousands of dollars Q Q

was given to students in an introductory statistics class during the first week of the course One question asked How stressed have you been in the last 2 weeks on a sca 10 with 0 being not at all stressed and 10 being as stressed as possible The students responses are shown in the frequency distribution How many students were involved in the study Click the icon to view the frequency distribution students Type a whole number Frequency Distribution Stress Rating 0 1 2 3 4 5 6 7 8 9 10 CHCELED Frequency 4 3 2 12 16 13 11 33 24 12 12 m

Consider the graph of the exponential function below 10 5 10 5 0 5 10 0 6 5 1 powered by desmos

Evaluate without a calculator a 5 b 23

Find all rational zeros of the following polynomial funct P x x 43 x 55 x X 7 7 x 13

You decide to purchase a car for 22 750 Assuming the sales tax is 5 5 of the purchase price find each of the following a What is the total cost including sales tax b If you make a down payment of 18 of the total cost find the down payment c Assuming you finance the remaining cost at an annual interest rate of 7 05 for 10 years find the monthly payment

The accompanying figure shows the highway fuel consumption mi gal for two different models of car How is the graph misleading How could it be drawn so that it is not misleading Click the icon to view the figure How is the graph misleading OA The graph is misleading because it does not use a uniform scale for the vertical axis OB The graph is misleading because the vertical axis scale does not start at zero OC The graph is misleading because the fuel consumption for each car is given in different units OD The graph is misleading because the height of each bar is proportional to the fuel consumption for the two cars but the area of each bar is proportional to the square of each car s fuel consumption Fuel Consumption Data mi gal uel consumption mi gal X

12 HW 71 The commuting times in minutes of an employee for ten consecutive days are listed below Find the median commute 67 67 72 76 72 73 68 A 73 minutes B 72 minutes OC 67 minutes D 71 minutes Question 15 3 1 10 72 72 HW O

Define and distinguish among mean median and mode Choose the correct description of the mean below SOCCE O A The mean is the middle value in a data set It can be strongly affected by outliers OB The mean is the most common value in a data set It can be strongly affected by outliers OC The mean is the most common value in a data set It is not affected by outliers D The mean is the middle value in a data set It is not affected by outliers OE The mean is the sum of all the values divided by the number of values It is not affected by outliers OF The mean is the sum of all the values divided by the number of values It can be strongly affected by outliers

A random sample of 30 college students is selected Each student is asked how much time he or she spent on homework during the previous week The following times in hours are obtained 16 20 21 25 16 15 24 17 20 25 20 17 23 24 21 22 15 19 16 24 22 19 20 21 15 17 20 17 19 23 Construct a frequency distribution for the data Type the frequency for each data value Hours Studied Freq

Use the given table to evaluate each expression in parts a through d if possible a f g 2 b f g 4 d c fg 2 a f g 2 7 Simplify your answer b f g 4 8 Simplify your answer c fg 2 Simplify your answer X 2 0 2 4 f x 0 7 10 14

The campus of a college has plans to construct a rectangular parking lot on land bordered on one side by a highway There are 680 ft of fencing available to fence the other three sides Let x represent the length of each of the two parallel sides of fencing a Express the length of the remaining side to be fenced in terms of x b What are the restrictions on x c Determine a function A that represents the area of the parking lot in terms of x d Determine the values of x that will give an area between 20 000 and 40 000 ft e What dimensions will give a maximum area and what will this area be A for x between 32 52 ft and 75 66 ft or 259 34 ft and 307 48 ft B for x between 32 52 ft and 80 66 ft or 259 34 ft and 307 48 ft C for x between 32 52 ft and 75 66 ft or 264 34 ft and 307 48 ft D for x between 32 52 ft and 80 66 ft or 264 34 ft and 307 48 ft e The area is maximum when the width is feet and the length is Type whole numbers HH y values A Se such that A UTU Type whole numbers c The area of the parking lot in terms of x is A x x 680 2x Type an expression using x as the variable d For what values of x is the area between 20 000 and 40 000 feet X A

The population of Stuart can be modeled by the function P 169880 001019t where t is the number of years since 2020 Use the above function to answer the following questions What was the population of Stuart in 2020 In what year is the population of Stuart projected to reach 25 482 Round the solution to the nearest w number U

C H 8 y 7 5 4 3 2 1 6 5 4 3 2 AB 1 2 3 4 5 6 7 8 9 6 D 1 2 3 4 X 5 Write the equation of a polynomial function that passes through A B C and D f x 4

Show that fog x is not equivalent to gof x for f x 9x and g x Find fog x fog x f g x fog x f 7x 9 fog x 9 7x 9 7 fog x Definition of composition Replace g x with its expression Use the definition of f x Simplify

The compound interest formula is given by T nt A P 1 7 where A is the accumulated amount after an initial investment of P dollars is invested for t years at annual interest rate r compounded n times per year Use the formula above to determine how long it will take an initial investment of 12 250 to grow to 51 450 if the account earns 14 interest per year compounded daily Round the solution to two decimal places Assume there are 365 days in a year The account balance will reach 51 450 after years

Graph the quadratic function f x x 4x 7 Give the a vertex b axis c domain and d range a The vertex is 2 3 Type an ordered pair Use the graphing tool to graph the function b The axis is x 2 Type an equation c The domain is Type your answer in interval notation 20

Solve the following exponential equation Use logarithms to express the solution in its exact form In addition use a calculator to approximate the solution 4 91 The exact solution is given by U The approximate solution rounded to four decimal places is given by

Solve the following logarithmic equation In addition use a calculator to approximate the solution 7log z 11 The exact solution is given by Z The approximate solution rounded to four decimal places is given by

y 1 2 3 4 X 5 Write down the equation of a polynomial function with the following properties As x y As x y 8 The number of different real roots is 4 The y intercept is positive f x

For the quadratic function f x x 2 4 determine the largest open interval of the domain a over which the function is increasing and b over which the function is decrea a The largest open interval of the domain over which the function is increasing is Type your answer in interval notation

Solve the inequality ite the 5x 2 4x 7 x 3 0 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Simplify your answer Type your answer in interval notation Use integers or fractions for any numbers in the expression OB The solution is the empty set

Find a polynomial of least possible degree having the graph shown 0 1 5 f x Type your answer in factored form

se the properties of logarithms to expand the following logarithmic expression as much as possible Where ossible evaluate logarithmic expressions In

Give the equations of any vertical horizontal or oblique asymptotes for the graph of the rational function x x 2 2x x 21 f x Select the correct choice below and fill in any answer boxes within your choice A 7 The vertical asymptotes are x 3 2 Use a comma to separate answers as needed OB There is no vertical asymptote Select the correct choice below and fill in any answer boxes within your choice OA The horizontal asymptote is y Use a comma to separate answers as needed B There is no horizontal asymptote W

domain of f Identify the equations of any vertical asymptotes Select the correct choice below and fill in any answer boxes within your choice OA x Simplify your answer Use a comma to separate answers as needed B There is no vertical asymptote Identify the equations of any horizontal asymptotes Select the correct choice below and fill in any answer boxes within your choice OA y Simplify your answer Use a comma to separate answers as needed B There is no horizontal asymptote 2 2 2

Find a polynomial of least possible degree having the graph shown 4 74 50 0 24 2 6 f x Type your answer in factored form

Equation 4 2 ex 1 x 52 2x 25 2 4 x 1 256 Answer Enter an equation in terms of x and y D

K Find a polynomial of least possible degree having the graph shown Use a leading coefficient of 1 or 1 f x Simplify your answer CITE 6 A H 5d 10 64 100

Graph the polynomial function Factor first if the expression is not in factored form f x x 8x 11x 20 Use the graphing tool to graph the function Click to enlarge graph Click the graph choose a fool in the palette and fol AY 40 32 24 16 8 8 16 24 32 E 40 A UJ

Find a polynomial of least possible degree having the graph shown Use a leading coefficient of 1 or 1 f x Simplify your answer CIB Ed 100 064

Calculate the distance between the points E 2 3 and C 6 7 in the coordinate plane Give an exact answer not a decimal approximation

Using the Intermediate Value Theorem show that the function f has a zero between a and b f x x 3x 2 9x 13 a 5 b 4 What is f 5

Find a polynomial of least possible degree having the graph shown 8 6 95 50 0 45 3 5 f x Type your answer in factored for

polynomial of least possible degree having the graph shown 0 1 U f x Type your answer in factored

1 In an arithmetic sequence the first term is 8 and the sum of the first 20 terms is 790 a Find the common difference

31 Given ATUV when ZV is the right angle and t 15 and v 18 the length of the leg u is x 32 How many values of x make 6x 36 6 x 6 a true statement O infinite values one value no values 33 Replace the with the correct symbol or which will make a true statement from the following expression

8 The cost of sending a package through first class mail is indicated in the table below Find the domain of this function relating weight of the package to mailing cost Weight ounces Cost 0 45 0 65 0 85 1 05 less than 1 between 1 and 2 between 2 and 3 between 3 and 4 O Domain 0 45 weight 1 05 Domain 0 weight 4 O O Domain 3 weight 4 Domain 0 weight 1

19 Two ordered pairs that are solutions of the equation 2y 6x 14 are O 7 14 1 10 O 7 14 4 19 O 7 14 1 5 O 7 28 4 19 20 Solve for y 6 3 y x

f x Simplify your answer Use integers or fractions for any numbers in the expression 12 RA 12

7 Find y when r 22 if y varies directly as a and y 40 when 11 84 39 O 85 76 78 83 O 80