Quadratic equations Questions and Answers

Part 1 of 2 curve y 4x 3 3x at the point 1 1 Sketch the curve

Use the graph of the function to identify its domain and its range Select the correct choice below and fill in the answer box to complete your choice OA The domain can be best described using interval notation The domain is OB The domain can be best described using the roster method The domain is x x X Use a comma to separate answers as needed 10 B 6 10 B 8

Find the logarithm using the change of base formula log 5 40

Write an equation for the hyperbol y 5 2 x 8 2 8 1

x 3lyl 3 Step 1 of 2 Find four points contained in the inverse Express your values as an integer or simplified fraction Answer

Suav wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp with a 19 angle of elevation from the ground How high will the ramp rise from the ground at its highest end

Vrite answer in fraction form 3 3 16x4 1 5x 60x5 18x7 2x 6x 57x 3x 4x 1 x 4 x6 8x5 31x4 28x 10x 8x 15 x 10x 12x 6x

Part D Find the average rates of change of T t over the intervals 0 t 6 and 6 t 12 Enter the correct answers in the boxes Round to the nearest tenth Show Hints 0 t 6 6 t 12

Suppose that an individual has a body fat percentage of 18 6 and weighs 143 pounds How many pounds of her weight is made up of fat Round your answer to the nearest tenth

In the table the values of T t decrease as the value of t increases As t you can predict that T t 7 4 1 0 8 5 2 9 6 3 the temperature of the freezer X

What angle in degrees corresponds to 14 2 rotations around the unit circle Enter the exact answer Angle Mi degrees

2 Find the zeros and their multiplicity for the polynomial function State whether the graph crosses the x axis or touches the x axis and turns around at each zero f x x 6x 9x

1 The daily profit in dollars of a specialty cake shop is described by the function P x 6x 312x 2880 where x is the number of cakes prepared in one day The maximum profit for the company occurs at the vertex of the parabola How many cakes should be prepared per day in order to maximize profit What is the maximum profit

9x 3x 9x 6x l g x 10 x 10 XI Xx 40x 10 10x 100 x 10 x 10 x 10 X 100 X 1 X 144 24X Why do you think that is h 3x 2 3x 2 BY 2 3x9x 7 6x 26X4 3x 2 3x 2 3x 2 9x 4 X 7X 8X 56 X 15X 56 i 5x 2 5 2 5x2510x 25x 10x 22 6x4 254722 25x2 5x 2 2 5X 3 5X 2 5x 5x 2 2 5x 2 2 Which of the problems above above resulted in a polynomial with only 2 terms

DIRECTIONS Use this information to answer Parts A and B x 12x 36 Consider the expression 2 216 Part A Show Hints Find the product Enter the correct simplified expression in the boxes 7 8 9 23 216 2 36

DIRECTIONS Use this information to answer Parts A and B 7p 20q 4rs 21p s Consider the expression Part A Find the product Enter the correct simplified expression in the boxes Follow ordering conventions when writing your simplified expression Show Hints

Determine the difference Find the answer in simplest form x x 6 Enter the simplified difference in the box 1 9 7 Show Hints

The decline of a bacteria population is modeled by the formula P 300 000 e 0 005t where t is measured in days How many days will take to the nearest day before the population P declines to 100 000 Use an algebraic solution and show your work 5 pt

Find the nth term an of the geometric sequence described below where r is the common ratio 87 64 r 2

aura is creating a triangular garden in her backyard by laying wooden edging and filling the space with soil She has already laid one side of th wooden edging measuring 21 feet in length Laura wants the garden to be an obtuse triangle which of the following is a pair of possible lengths for the other two sides of the garden O A 6 feet and 14 feet OB 10 feet and 24 feet O C 20 feet and 29 feet D 22 feet and 28 feet

Prove that the points of the quadrilateral create a rhombus A 3 0 B 0 4 C 3 0 D 0 4

Use a graphing utility to find the quadratic function of best fit for the data 35 45 55 65 75 109 167 245 342 451 25 64 y Type an expression

Determine if the following function has an invers Answer r x X2 Or has an inverse function Or does NOT have an inverse function

retires A woman with her employer s matching program contributes 500 at the end of each month to her retirement account which earns 5 Interest compounded monthly When she after 41 years she plans to make monthly withdrawals for 33 years It her account earns 7 interest compounded monthly then when she rebres what is her maximum possible monthly withdrawal without running out of money The maximum possible monthly withdrawal is approximately Simplify your answer Round to the nearest cent as needed COLLE

Use the power series n 0 to find a power series for the function centered at 0 f x arctan 9x 00 f x 1 Ix 1 n 0 Determine the interval of convergence Enter your answer using interval notation

ces Joey s Bike Shop sells new and used bicycle parts Although a majority of its sales are cash sales It makes a significant amount of credit sales During Year 1 its first year of operations Joey s Bike Shop experienced the following Sales on account Cash sales Collections of accounts receivable Uncollectible accounts charged off during the year Required a Assume that Joey s Bike Shop uses the allowance method of accounting for uncollectible accounts and estimates that 1 percent of Its sales on account will not be collected Answer the following questions 1 What is the Accounts Receivable balance at December 31 Year 1 2 What is the ending balance of the Allowance for Doubtful Accounts at December 31 Year 1 after all entries and adjusting entries are posted 3 What is the amount of uncollectible accounts expense for Year 1 4 What is the net realizable value of accounts receivable at December 31 Year 1 b Assume that Joey s Bike Shop uses the direct write off method of accounting for uncollectible accounts Answer the following questions 1 What is the Accounts Receivable balance at December 31 Year 1 2 What is the amount of uncollectible accounts expense for Year 1 3 What is the net realizable value of accounts receivable at December 31 Year 1 Complete this question by entering your answers in the tabs below 257 800 616 800 244 910 1 279 Required A Required B Assume that Joey s Bike Shop uses the direct write off method of accounting for uncollectible accounts Answer the following questions 1 What is the Accounts Receivable balance at December 31 Year 1 2 What is the amount of uncollectible accounts expense for Year 1 3 What is the net realizable value of accounts receivable at December 31 Year 1 Show lessA

a The graph of y f x is shown Translate it to get the graph of y f x 2 b The graph of y g x is shown Translate it to get the graph of y g x 5 Part a Part b

Three parts of a SSA triangle are given There may be 0 1 or 2 solutions to this triangle Compute the area s of the possible triangles If there are no solutions enter 0 for both the larger area and the smaller area If there is one unique solution enter the area for the larger area and enter 0 for the smaller area If there are two solutions enter the corresponding areas a 10 c 11 A 58 AT b larger area smaller area A a h

4 5 The function fis represented by the equation f x x 2 x 3 and the table provides some values for the quadratic function g X 5 3 g x 3 1 Which of the following statements is true Select all that apply A The sum of the zeros of f x is less than the sum of the zeroes of g x B The sum of the zeros of f x is greater than the sum of the zeroes of g x C The x coordinate of the vertex of f x is less than the x coordinate of the vertex of g x D The x coordinate of the vertex of f x is the same as the x coordinate of the vertex of g x E The y coordinate of the vertex of f x is less than the y coordinate of the vertex of g x F The y intercept of f x is less than the y intercept of g x G The y intercept of f x is greater than the y intercept of g x C D 1 3 The accompanying table shows profits for a new model of headphones as a function of price x Price 16 17 18 19 20 ofit thousands 240 223 200 173 140 Part A Find the model that represents the table above Round the values to the nearest hundredth REE VNSYS

Consider the graph below which shows the path of a parabolic water arc Here the x coordinate is the distance the flow of the water is from the water source measured in feet and the y coordinate is the height of the water arc also measured in feet Height of the water 100 6 IN IN 2 9 10 Distance in feet from the water source 12

Write the equation of the line that contains the points 1 3 and 5 1 in slope intercept form O y x 2 O y x 3 y x 4 y x 4

Calculate the exact distance between the points 5 1 and 7 3 14 O2 37 O 2 13

Write the equation of a circle whose center is 6 7 and which has a radius of 3 O x 6 y 7 6 x 6 y 7 3 O x 6 y 7 9 x 6 y 7 9

13 CHALLENGE PROBLEM Jim Smith invests 2 500 000 in a prime seaside 3 unit strip mall He has a 500 000 down payment Kate s Kites and Sandy s Seashells each occupy a 1 200 square foot unit Seaside Realty occupies the 2 000 square foot unit The units rent for 8 33 per square foot per month The annual mortgage interest is 175 000 depreciation is 3 5 of the purchase price and taxes insurance repairs and upkeep total 125 000 Determine the annual a net income and b yield

1 Sam Clark purchased a four unit apartment for 845 300 He made a down payment of 95 000 and rented each of the four units for 2 750 per month His annual expenses were mortgage interest of 46 200 depreciation of 3 of the purchase price and taxes repairs insurance and miscellaneous totaling 52 425 a What is the annual net income b What is the annual yield c What monthly rent should he charge if he desires an annual yield of 10 00

12 Clara Teague buys a house for rental purposes for 115 800 with a 25 000 down payment Her annual expenses total 12 430 What monthly rent should she charge if she desires an annual yield of 8 00 CHALLENGE PROBLEM Jim Smith invests 2 500 000 in a prime seaside E

survey is carried out at the University of North Carolina Chapel Hill to estimate the propor I graduate students living on campus in the current term Of the 14 855 graduate students rolled at the campus a random sample of 300 was surveyed What is the population All graduate students in North Carolina The random sample of 300 students

Graph the following 3x 2y 10 on the set of axes below Identify the slope and y intercept

10 A pizzeria charges 14 for an extra large pizza and 2 for each additional topping If x represents the number of additional toppings ordered write a function that could represents the total cost of the pizza If you decided to get peppers onions and sausage how much would the pizza cost

Find the products in simplest form 8 5 21 16

6 The formula for the volume of a cone is V r h Find h in terms of Vand r

4 The formula for the area of a trapezoid is Ah b b find b2 in terms of A h and b row wode Jaum uoY novig od lliw ibero leiting on moldong done tomo be 999 noitesup soods slqitlum novo emitu In no and en x dow 88 x IS E noiteups dl gaivio new Sqose sent ensind esititui vnoqorida Vilep to 2 insbl ovitcoilqiluM 2 qol vidinaid vilupa tovoqo19 noitibbA

2 If f x 300 76 and g x 100x 7 for which value is g x f x 1 x 1 2 x 2 228 107x 3 x 3 4 x 4 you foiqad tot drini 1 SHOW YOUR WORK 01 1121 of x 30c C 76 no 004 var gcx5 100x 7 3 The ages of Kristen and her two siblings Julie and Matt are consecutive even integers The sum of their ages is 90 Find the ages of Kristen Julie and Matt

Write the slope intercept form of the equation with slope 7 and y intercept 0 2 The equation is

A company experiencing rapid growth can be short of cash despite earning substantial net income True or False True False

13 Write the equation for the graph shown below The parent function is f x x shown as a dotted graph Equation T 12 11 10 9 8 7 16 54 210 6 7 1

nsider the graph of f x hat is the average rate of change of f x from x 0 to x 9 Please write your answer as an integer or simplified fraction Enable Zoom Pan 201 0 17 16 12 00 8 IN 4 9 7 11 9 7 10

What is the average rate of change of f x from x 7 to x 3 Please write your answer as an integer or simplified fraction f x 7x 8 Answer

Arrange the solution steps in the correct order 63y 7 234 6 y 227 In 63y ln 227 In 227 y 3 3y In 227 In 6 y In 227 In y

Consider the function g x log x 1 8 Part A Identify the transformations of the graph of the parent function that produce the graph of the given function g Select the words from the drop down lists to correctly complete the sentence Show Hints There is a reflection across the x axis and a translation unit Part B Identify the asymptote of the graph of g x Enter the correct value in the box Show Hints to the left and 8 units I dow