Quadratic equations Questions and Answers

Given the formula and graph of a function find the formula and graph after transforming the function as indicated 4 shift the graph 1 unit to the right and then stretch the graph by a factor of 2 and reflect it across the x axis HHH7 y x y x 1

Find all the real number roots of the equation Give an exact exp 1 3x 2 1 3x X log T 22 6 X

Begin by graphing the absolute value function 10x x Then use transformations of this graph to graph the given function g x x 21 4 What transformations are needed in order to obtain the graph of gox from the graph of f x Select all that apply A Reflection about the x axis B Honzontal translation C Reflection about the y axis D Vertical stretch shrink E Vertical translation F Horizontal stretch shrink Choose the correct graph of g x below OA Q P B odt km OC 300

Write the quantity using sums differences and constant multiples of simpler logarithmic expressions Express the answer so that a log10 x 5 x 8 b In x x 5 x 8 x 5 x 8

The table below represents a an x y X 14 2 10 3 20 4 34 Select one O a Quadratic O b Exponential O C Linear Quadratic and Exponential model

If the population growth P of a sample of bacteria after x days is expressed as a function P x 4 4 What is the population of bacteria after 3 days

What is the domain dhe function f x 2 Select one Oa O b 1 5 OC O d 0 DE

The table below represents a an X Y 1 2 4 3 4 9 16 5 25 Select one a Quadratic b Linear c Exponential d Cubic model

In the vector space of all real valued functions find a basis for the subspace spanned by sin 2t 1 cos2t cost sint cost O sin 2t cost sint O sin 21 1 cos 2t costsin t sin 24 1 cos 2t cost O 1 cos 2t cost sint cos t Ofcost sint cos t 1 cos 2t cos t

3 Given f x 2x 3 x 5 a State the domain and range of f x b Find f x show all work c State the domain and range of f x

Point P 8 4 is on the terminal arm of angle in standard position Calculate cose Select one a b cose d cose C cose cose 1 2 10 2 5 5 1 10 4 5

Match each word with its definition or notation Assume a 0 Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE Parabola Vertex Axis of symmetry Standard form of a quadratic function E III E The vertical line through the vertex of a parabola P x ax bx c The highest or lowest point of a parabola The shape of the graph of a quadratic function Rivi alx h

8 pts Find the area of quadrilateral ABCD Round values to 2 decimal places D 8 ft A 75 B 12 ft 16 ft 18 ft

Q17 Obtain y 4 2 and y 4 4 given series method dy dx 1 x y y 4 4 taking h 0 2 using Taylor

Solve for x 2x 1 x 1 Select one 2 Ob 2 0 OC 0 No Solution

7 Consider the expression x cose x cos20 x cos38 x cos730 where 18 then answer the following If coefficient of x is equal to COS k then k is where k N Magnitude of x71 is equal to 8

a Work out in terms of the curved surface area of the frustum b Work out in terms of the total surface area of the frustum 16 cm 4 cm 2 cm 10 cm

Construct a model of population flow between metropolitan and nonmetropolitan areas of a given country given that their respective populations in 2015 were 261 million and 44 million The probabilities are given by the following matrix to from metro nonmetro 0 99 0 02 metro 0 01 0 98 nonmetro Predict the population distributions of metropolitan and nonmetropolitan areas for the years 2016 through 2020 in millions to four decimal places Let x through x represent the years 2016 through 2020 respectively x 261 21 43 79 259 47 45 53 41 257 78 47 21 256 15 48 84 254 57 50 43 11 11

24 Find the Laplace Inverse for the following Function using Partial Faction S 10S 21 s 3 s 3 F s

X X 2 Identify the key components of the graph of the function If no intercept can be found enter none in each of the blanks for that part f x 2 x 1 4 3 Vertex Type your answer here b Y intercept Type your answer here c X intercepts d The parabola opens e The vertex is a our responsa hara f The domain is Write you Write your Enter the domain and range in interval notation Write your Type your answer here sa hara 1 Type your answer here Write your response here Gara up down maximum minimum point and Enter the word infinity for and infinity for

Hidhe Use the product rule for logarithms to find all x values such that log 2x 10 log x 3 2 spolicy CV I

Rewrite the equation in exponential form log 127 a log 4 127 Preview log 127 syntax error this is not an equa

Given P x a x h k where a 0 match each expression with its correct impact to the graph of the function Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE a 0 a 0 E E h is the maximum value of the graph k is the minimum value of the graph k is the maximum value of the graph

y sec 2 For which values of x is the function positive 6 x 2 O 2 x 2 02 x 6 O 0 x 4 4 x 4 The answer is not among the choices given

52 The following function is written in the form f x ax bx c Fill in each blank with the appropriate number related to this function f x 2x 8x 5 a The value of a is b The value of bis Type your answer here Type your answer here c The simplified value of x b 2a is Type your answer here

Find f 10 f 10 Find f 2 h Expand and simplify your answer f 2 h Find f x h Expand and simplify your answer f x h f x h f x h Find f x h f x h Complete the description of the piecewise function graphed below 6 5 4 3 7 6 5 4 3 2 1 1 f x 1 2 3 4 5 5 1 0 J Expand and completely simplify your answer 0 OB if 6 x 3 if 3 x 2 if 2 x 6

Match each term related to P x a x h 2 k where a 0 to its correct expression Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE Axis of symmetry The x value of the vertex The y value of the vertex The x value of x intercept s 4 The solutions of P x 0 Eh Ek III x h

Let P x x 3 4 Match the parts of the graph to the correct expression Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE Domain Range Vertex Maximum value of the function Minimum value of the function x intercepts 1 0 and 5 0 III E 3 4 None 5 0 and 1 0 3 3 4 4

Let f x x x 6 and g x x 4 Find the value of of fog 5 Type your numeric answer and submit

Match each function with its correct expression using the following functions f x 1 x and g x x 4 Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE f g x f g x fg x 1 x E E x x 4x 4x III x x 3 x x 5 1 X X 4 x x 4x 4 4

Homework Unanswered Find f x h f x h f x 10x 9 Type your numeric for the function

Choose the equivalent expression s for 572 07 07 L Select one or more 1 5 O b 1 O c a O d 5 53

16 on 6 5 4 3 2 1 1 24 3 4 y 1 2 3 4 5 6 Ad Write an equation for the function graphed above

Which of the following graphs is not a function Select one a Ob 4

E The graph of f x x is shown below with five specific points labeled Plot the location of each of these five points after the graph is shifted left two units 24 11 KALH 1234 b

Write an equation any form for the quadratic graphed below Ve 5 4 3 2 y 3 2 11 30 4 Question Help Video Message instructor

Match each function with its definition Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE f g x f g x fg x x fog x 4 III E E III f x g x f x g x f x g x f x g x f g x

Let f x 3x 5x 1 and g x 4x 1 Find the value of f g 2 Type your numeric answer and submit

Draw the graph of the function f x 2 x 1 Select one a O b O c 2

Let f x X 4 X 2 and nd h x x Find the value of f o h 9

sketch the projections of the curve r t 2sin t t cos t onto the three coordinate planes the xy xz and yz plane

Solve the equation and enter the solution set below If there is more than one solution write them in order from smalle largest and separate the solutions by a comma Do not enter any spaces in the answer Example 1 5 8 2 2 4 2

What is the value of the exponent when simplifying the following expression 67 Select one or more a 6 63 b 6 6 100 D C 6 63 d 66 e 8 of 1 3 4 A

Match each function with its domain Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE f x x 4 f x 2 x 1 f x x 2 f x 1 x 2 00 2 2 00 2 00 0 00

Teresa has reward money for 30 off any purchase at her favorite department store The store takes 15 off any item purchased during its Early Bird sale Letx represent the listed price of an item in the store a The function P X rep P x Write your response here b The function D x represents the price of an item purchased during its Early Bird sale D x represents the price of an item if purchased with reward money Write your response here c Teresa buys an item during the Early Bird sale and is also permitted to use her reward money The cashier applies the discount first and then applies the reward money The function Po D x represents the final cost of the item PoD x Write your response here d What is the cost of a 75 item before tax if Teresa purchases an item during the Early Bird sale and the discount is applied before the reward money DOP x Type your answer here e The function DoP x represents the situation in which the cashier applies the reward money before the Early Bird discount Enter the simplified form of the function Write your response here Enter the simplified form of the function with no spaces f What is the cost of a 75 item before tax if the reward money is applied before the Early Bird discount

Condense the expression to a single logarithm using the properties of logarithms 3 log a 4log x 2 log Preview

Find the second derivative y 6x 3x O a y 4 6x 3x 2 3 4x 1 6x 3x 5 3 12x 3 O b y 2 5x 5x 4 5 2x 1 5x 5x 10x 5 y 4 4x 2x 2 4x 1 4x 2x x 2 O C

Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE 4x 5 6x 2 4x 5 6x 2 4x 5 6x 2 4x 5 6x 2 E E E 62x 10 E 10x 7 26x 10 24x 22x 10 24x 38x10 2x 3

Identify the following as either the intersection of two sets the union of two sets or no intersection x 0 and x 5 Select one a No intersection b Union c Intersection

For this problem let P 3 3 Find P2x