Quadratic equations Questions and Answers

Estimate the solution of the equation from the associated graph Check by substituting into the equation 2x 7 x 1

Solve the following equation using the quadratic formula 2x 2 15x 8 The solution set is Type an exact answer using radicals and i as needed Use a comma to separate a

Use a graph to find all of the solutions to the inequality below z 5 2 2 Type your answer in interval notation without spaces use inf for infinity For example 2 inf

Consider the functions F and G as shown in the graph to the right Find the domain of G F What is the domain of G F Type your answer in interval notation Ay 104 8 n 4 6 2 0 2 4 G F 6 8 10 12 14 365 G E

Write the explicit formula for the arithmetic sequence below 6 1 4 9 an Type your answer without spaces Try writing the recursive formula in your notebook for additional practice

A rectangular plot of land is designed so that its length is 8 meters more than its width The diagonal of the land is meters To the nearest tenth of a meter what are the dimensions of the land The width of the land is meters and the length of the land is Round to the nearest tenth as needed meters

The revenue R received by a company selling x pairs of sunglasses per week is given by the equation R 0 1x 30x a Find the values of x 19 and x 25 b How many pairs of sunglasses must be sold in order for the revenue to be 2000 per week c How many pairs of sunglasses must be sold in order for revenue to be 2250 per week a Find the values When x 19 R S

e the Pythagorean Theorem to determine the value of x and the measurements of all sides he right triangle shown to the right e a comma to separate answers as needed A For the single value of x 30 d the measurements of all sides of the right triangle Select the correct choice below and fill in the answer es to complete your choice R th x 102x 10 the lengths of the sides of the triangle are X

16t 160t a baseball is projected upward from ground level with an initial velocity of 160 feet per second then its height is a function of time given by s What is the maximum height reached by the ball The maximum height reached by the ball is feet

Find the vertex form of the quadratic function for the following

Make a table of values for the following equation Then graph the equation y x 4 Complete the table of values below X 3 1 0 1 3 Simplify your answers y

1 2x 3x 2 x 3 x 6

24 2x 3x 2 x 3 x 6

2 Unit 1 Lesson 5 Cumulative Practice Problems 1 Match each sequence with one of the definitions Note that the starting value part of a complete recursive definition is missing so as not to give away the solutions 1 6 12 18 24 a n 7 a n 1 2 2 14 98 686 b n b n 1 3 160 80 40 20 c n c n 1 6 Term Practice Lesson 5 0 1 2 Write the first five terms of each sequence Is it arithmetic geometric or neither a n 1 3 for n22 7 4 1 2 5 a a 1 7 a n b 1 2 b n 2 b n 1 1 for n 2 2 1 1 3 5 c 1 3 c n 10 c n 1 for n 2 3 Complete the table below by referring to the graph of 2 sequences Seq B 1 2 2 3 6 4 5 b ices and Functions C Seq A 1 2 5 8 2 a 4 8 16 b Period Date 2023 09 13 C 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 1Q NM 2 3 A B A For Sequence A describe a way to produce a new term from the previous term B For Sequence B describe a way to produce a new term from the previous term 2 Fumlain how you know

Use the slope intercept form to write an equation of the line that passes through the given points Use function notation where y f x 20 2 3 and 7 11 20

5 Solve for x and y 2y 3 8x 27

The function D p gives the number of items that will be demanded when the price is p The production cost C a is the cost of producing x items To determine the cost of production when the price is 10 you would Solve C D p 10 Evaluate D C 10 Evaluate C D 10 Solve D C x 10

Solve the quadratic equation by completing the square x 10x 2 0 Choose the appropriate process for rearranging the equation if nee Type an integer or a simplified fraction O A x 10x 2 0 x 10x 2 x 10x OB x 10x 2 0 x 10x 2 17 0X 10 X O c x 10x 2 0 x 10x 2 10x x X 2 11 1 15 5 D x 10x 2 0 x 10x 2x2 10x 2

In 2009 President Obama launched a nationwide initiative to end homelessness in the U S by 2020 The homeless are a vulnerable population with limited access to health care and poor health outcomes To allocate sufficient federal and local resources to eliminate homelessness U S cities conduct an annual survey to estimate the number of homeless persons living within major cities The City of Boston s Emergency Shelter Commission ESC conducted a survey of homelessness on the night of January 25 2017 Volunteers counted the number of homeless persons living on the streets in emergency shelters for individuals or families in domestic violence programs in residential mental health or substance abuse programs transitional housing and in specialized programs 1 Which of the following best describes the homeless population in the City of Boston a Dynamic population b Fixed population 2 Which of the following describes the homeless population that took part in the ESC survey on January 25th a Dynamic population b Fixed population 3 The 2015 Homeless Census counted 3 456 homeless persons in Boston The 2016 homeless census counted 3 384 homeless persons in Boston The size of the population in Boston was 665 984 in 2015 and 673 184 in 2016 From 2015 2016 did the burden of homelessness a Increased by more than 1 percentage point b Decreased by more than 1 percentage point c Stayed approximately the same d Cannot determine from this information

Multiply 2 5i 3 i Enter your answer in standard form in the

Which expression is equal to 3 i 5 6i O 2 5i 07 0 7 O 4 11i

Evaluate each function Round to the nearest hundredth if necessary TWO DIGITS 9 w n n 0 7n Find w 6 6 10 10 p x x 2 4 Find p 1 7

What are the real and imaginary parts of the complex number 6 2i Enter your answers in the boxes The real part

Which expression is equal to 2i 4 i O 28i 08 2i O 8 2i O2 8i

Which expression is equal to 8 3i 3 4i O 11 7i 04 O 4 O 5 i

Determine h x for the following function answer 3x h x x 4x 9

6 6 h a 3 8a 2 Find h 4 6

7 Evaluate each function Round to the 5 w x 3 8x 1 1 Find w 5 7 Evaluate each function 7 w x 2 Find w 1

The table below illustrates the growth in worldwide Internet use Year x 2001 0 2002 1 2003 2 2004 3 2005 4 2006 5 2007 6 2008 7 2009 8 2010 9 Number of Internet Users Worldwide y in millions 495 677 785 914 1036 1159 1393 1611 1858 2084 Estimate Sources International Telecommunication Union ITU Statistics a Without using a graphing calculator model the data with a linear function Let the indepe the number of years after 2001 that is the data points are 0 495 3 914 and so on Sho ution found in part a estimate the number of Internet users worldwide in 2

Evaluate the expression 144 4 7 4 144 4 7 4 Simplify your answer

Choose the INCORRECT statement about the function below 4 A B C D y 30 20 10 21 0 10 20 30 40 1 2 X 33 x 3 The function has two relative maximum values There are no intervals where the function is constant The function has two relative minimum values The function is increasing from 1 x 1

Simplify the expression 36 64 V 36 64

Solve the equation Check your solution 5x 16x 9 11 3 The solution set is Simplify your answer

Solve the equation Check your solution a 2a 4 Gl 3 2

Evaluate the expression 3 16

Simplify the expression 64 225 64 225 Simplifi Quor Tuno di

Evaluate the expression 25 4 3 2 25 4 3 2 Simplify your answer

Simplify the expression 49 8 64 64 Select the correct choice below and fill in any answer boxes in your choice O A 49 64 64 Simplify your answer Type an exact answer using radicals as nee B The answer is not a real number 8

16 Cem 15 Can x ya ndad r Cem Can n ya nda iken Can n do mas na 5 y l vard Buna g re Can n bug nk ya ka t r A 5 B 6 C 7 D 8 E 9

7 Find the domain of y 2 x 3 x 7

If tan 0 24 10 sin 0 equals cos 0 equals 8 qual 0 0 T 2 the

1 The complete graph of a function is shown below a What is the domain of the function b What is the range of the function 10 9 8 7 6 5 4 3 2 1 1 0 1 2 3 4 5 6 7 8 9 10

A term of the binomial expansion mx y where m is a positive integer is 640x The value of mis 640x y C mx 6 2 y 3 4 Jm3

5 points Let n and i be nonnegative integers Prove the following equality by nduction on n n 1 2 i 1

sider the below matrix A which you can copy and paste directly into Matlab The matrix contains 3 columns which represent the final grades in a course with 3 sections of equal size The first column is C01 the second is CO2 and the third is C03 A 100 100 29 87 17 91 20 07 66 17 63 35 86 56 89 68 68 06 100 55 75 37 91 30 26 65 93 23 78 71 66 100 84 07 14 71 40 11 15 48 72 34 36 31 76 22 25 79 34 89 50 68 49 43 41 61 94 9 57 32 100 94 77 99 28 100 100 100 73 73 72 96 13 65 100 57 09 100 70 67 100 34 73 95 3 100 80 76 40 03 100 54 01 99 22 100 17 66 54 74 100 87 95 100 100 97 04 71 29 65 18 96 6 63 67 47 44 15 97 40 72 44 35 69 96 74 26 35 75 56 27 52 19 100 97 4 100 83 5 100 100 16 47 55 12 100 29 83 84 45 88 65 100 95 99 25 95 20 59 55 22 100 84 73 65 02 61 85 81 62 97 56 67 76 15 57 100 94 75 100 12 76 45 91 53 71 77 95 55 19 17 63 24 22 100 17 75 100 31 28 44 98 84 65 100 62 21 58 91 25 41 75 68 68 66 96 35 19 34 38 39 61 32 93 48 49 13 100 68 45 50 5 100 78 03 94 63 42 24 58 93 56 3 100 55 04 57 7 80 43 78 85 36 79 100 70 40 46 100 89 96 50 08 85 42 86 9 93 31 56 56 15 3 29 98 73 58 32 78 17 91 40 37 36 94 53 71 94 95 17 45 41 17 63 07 55 34 97 53 79 5 75 01 72 87 100 70 19 94 63 31 31 25 68 54 15 81 26 71 31 28 4 55 48 43 09 77 56 90 36 87 84 42 45 82 67 80 5 12 07 99 13 42 51 45 100 63 14 37 59 100 59 81 71 2 66 44 98 35 60 8 67 17 38 45 100 89 78 24 44 100 75 56 100 34 91 76 39 60 16 74 52 100 44 58 82 16 72 05 27 16 78 08 100 15 59 100 74 01 22 73 93 94 100 100 100 59 26 100 43 27 91 8 72 94 28 45 85 48 38 7 99 78 34 82 62 42 21 43 97 53 35 41 58 85 68 32 100 100 81 15 71 68 51 7 38 23 31 76 67 92 100 41 2 35 82 100 100 22 44 27 51 15 53 51 31 21 41 99 47 52 49 28 36 78 7 16 48 100 20 73 100 41 62 65 92 49 36 100 100 76 3 100 100 91 09 41 76 45 04 100 63 61 66 81 71 48 86 51 51 05 19 24 88 14 16 51 20 61 94 52 100 88 95 69 56 55 81 22 83 100 49 92 25 78 67 5 90 65 100 68 51 100 60 39 62 57 99 37 75 81 100 83 08 38 63 60 5 51 12 53 65 73 41 39 37 44 13 98 65 79 24 82 17 60 13 67 2 59 74 100 100 83 19 92 65 32 72 53 16 78 18 96 56 27 92 91 08 99 5 54 22 85 44 100 27 56 98 48 100 56 71 88 02 54 67 44 25 21 81 100 44 83 31 57 89 71 100 39 09 42 05 95 15 100 25 58 74 44 100 82 92 59 2 100 95 1 82 56 37 68 83 46 89 23 80 64 25 95 97 39 25 29 21 82 77 21 95 52 67 39 69 82 65 78 35 08 93 38 48 87 100 70 36 79 35 85 72 100 75 8 77 31 97 77 56 13 41 28 45 05 74 100 94 57 85 57 85 17 51 89 70 24 89 76 18 53 21 07 41 5 15 39 41 77 96 59 100 88 95 73 60 78 100 100 88 2 66 62 42 28 19 94 100 100 66 19 48 18 41 3 32 54 100 16 64 49 45 79 18 33 59 61 03 88 45 77 73 63 07 100 100 38 68 49 92 18 52 50 98 34 33 75 83 91 89 3 19 51 76 9 47 24 20 11 100 80 75 19 45 50 18 100 61 46 65 03 84 52 54 03 74 84 89 36 43 62 76 18 100 55 81 60 68 100 100 60 06 77 33 86 73 42 24 25 74 100 33 22 68 44 100 99 88 91 91 81 77 31 15 82 76 100 48 08 100 68 54 97 3 100 100 100 49 39 62 57 59 26 95 36 49 34 100 79 02 16 27 91 61 33 45 87 5 63 06 100 91 81 66 33 22 57 72 27 100 73 94 100 88 93 100 100 100 53 15 61 41 54 46 56 53 76 72 37 18 100 34 6 79 9 100 a Use the colon operator to extract the marks from C03 and then find the average of those marks using the sum and length commands b Use vertical concatenation to create a single column vector consisting of all of the marks from all 3 sections

1 Find the solution set to each inequality Express the solution in set notation AND graphically on the number line a 2x 10 ZI X 5 Solution Set 4 3 2 c 6x 9 1 5x49 4x ax 4x 2 3xx9 3 M Im b Solution Set 3 3 t 2 1 30 b 15x 45 15 15 2 X 31 32 2 5 1 0 Solution Set d 6x 5 7x 4 7x F7X 18 5847 Solution Set T 10

Use logarithms to evaluate 895 73 486

Identify the vertex and leading coefficient Then write the expression as f x ax bx c f x x 4 2 5

3 Angles of Elevation Depression Be sure to show any and all work a 5 pts If we have a point 6 14 on a graph and a line that passes through it at an angle of elevation at 60 degrees what is the function created by that line b 5 pts We know that the distance between us and a pole is 50 yards and the height of the pole is 20 yards as well What is the angle of elevation between us and the pole c 5 pts How close are we to a wall if our eyes are 5 ft above the ground creating an angle of depression to the ground that is 59 Degrees d 5 pts What are the angles of both corners in a right triangle if both sides have equal length

Solve the equation Check your solution 6 1 2 12