Quadratic equations Questions and Answers

Solve log 5x 4 3 O 11 809 11 5 O 199 2

Select the logarithmic equation after a vertical compression by a factor of 13 and a reflection over the y axis Oh x log x f x log x O g x log x Oj x log x

log 3x 1 log 4 2 O 1 67 O 133 O 1 365 O 34 33 Question 22 Solve 10 x 16 O 15 3 O 9 082 146

Select the inverse of f x f x ln x O f x log x O f x f x ex et

Consider f x 3x 1 X 0 1333 4 1 What is f 3 O f O f 3 f f 3 f x 1 8 1 3 3 0 3 8 4 Of 3 3 O f 3 cannot be calculated

Which of the following is a factor of 3 h x x 2x 4 O x 1 x 1 x O O x 2 x 2

f x 6 1 g x log x 1 Of g x log 6 1 1 Of g x 62 log x Of g x 6x 1 log x 1 Of g x 6log x 1 1 Question 14 Select the inverse of f x x ln x O f x log x f x e ex 4

1 361 O 3 698 8 516 Question 7 Rewrite in logarithmic form a c O log c a O log a c O log b c

What is the value of log 81 O 0 212 O 72 02 C O

log 25 O 2x O 5x O 5 O 22 Question 10 Simplify log3 4x log3 x 1 O log 5x 1 O logo 4x 4x O log 5x 1 2

What would you type into a calculator to evaluate log19 21 log 19 log 21 Olog 21 19 O log 19 21 log 21 log 19

How would you rewrite log 99 O In99 O loge 99 O log 99 log 00

What is the value of In e Why O 15 154 because the base of the log is e so ee 15 154 O e because the base of the log is 1 so e e O 0 because the log has no base O 1 because the base of the log is e so e 2

What is the value of log6 1 and why O O because 6 1 1 because 6 1 6 O 6 because 1 is the result of 6 and 6 being inverses O because 6 1

la c 5 85 3 50 h c represents the total charge for babysitting and h represents the number of hours the child is kept What is the amount Joe should pay when his child is at the babysitting service for 6 hours

Solve the system with the addition method 9x 7y 28 x 9y 52 Answer x y Preview a Preview y

Unit 6 Lesson 10 A rotation takes P to Q What could be the measure of the angle of rotation in radians Select all that apply YAQ P X

Find the missing side or angle Round to the nearest tenth A 72 C 50 a 40 c

For questions 12 15 prove the trigonometric identity 12 1 sin2 cos sing 13 tan 135 a tana 1 tana 1

Q18 What is the value of variable y in the following system Hint Cramer s Rule is suggested 2x y z 3 x y z o x 2y z 0 a d 6 6

0 Solve each equation for 0 0 360 You may need your calculator but remember that your calculator only gives one answer Most of these problems have more than one answer Think about all four quadrants Homework Help a sin 0 5 c 4 tan 0 4 0 b cos 0 5 d 3 sin 0 1 3x 2 5 Verify algebraically that g x 5 2 is the inverse function of f x 3 2011 The roots of a polynomial are given below Find two linear factors and the corresponding quadratic factor Homework Help a I 2 3 x 2 3 b x 2 i z 2 i Joanne was making repairs to her deck and needed to buy some supplies She purchased two posts three boards and four piers for 52 When she needed more materials she went back to the lumberyard and bought one post and five boards for 13 Realizing she did not need the piers she made a third trip in which she bought three more boards returned the four piers and ended up with a refund of 34 What was the cost of each item Homework Help

g x f f x dx as three points considering the interval 0 2 using Trapezoidal Rule and Simpson 1 3 Rule A calculate the exact results and compare the methods in terms of error values 1 x 1 x f x x ex

70 76 May 1 2023 Name 9 70 Represent the solutions to the inequalities below on a number line a 3x 2 10 c 2 x 2 10 x b 5x 1 3x24x 5 d 4 x 3 5 7 9 71 Algeria has decided to take out an advertisement in the U N newspaper Liberty Daily The newspaper charges a base fee of 1200 for an ad There is an additional fee of 300 for every inch in height If Algeria is willing to spend any amount up to and including 2700 what choices does the country have for the height of the ad 9 72 If the graph of an exponential function passes through the points 1 6 and 4 48 find an equation of the function Refer to the Math Notes box in this lesson if you need help

9 50 Solve 10 3x x A x 3 B x 2 x 5 C x 2 x 5 D x 10 Which of these shows the correct graph of the radical function g x x 1 D

57 Solve x 2 1 A x 9 C 58 Which of the following graphs represents an exponential equation A B Ay 2 4 x 2 X 9 B x 1 C x 0 D 4 8 Ay 6 4 8 4 4 2 x D x 3

51 52 Simplify completely 20x4 A 2 5x4 Identify the correct form of the Quadratic Formula b b 4ac 2a A A x C C x B 10x b b 2ac 4a 53 Identify a b and c for the following equation 2x 4x 2 a 2 b 4 c 2 C 2x 5 a 2x b 4x c 2 B B x D D x a 2 b 4 c 2 a 2 b 4 c 2 D x 20 b b 4ac 2a b b 2ac 4a

48 Simplify completely 200 A 2 10 49 Simplify completely A 5 B 10 2 A 36 B 50 Simplify completely 3 2 B 6 C 100 2 antalur y to gang od nefle wod impoteal of mourninselbs C 5 C 18 D 20 118 D V5 CA D 12

Match the function below with its graph 40 g x x 3 g x x 6 g x x 2 g x 2x 6 I A C 41 42 43 6 6 4 4 4 6 8 10 10 8 6 4 2 4 4 6 6 x B D 6 6 4 4 2 10 8 2 8 112 2 4 4 6 6 x x

Algebra 9 2 1 50 55 April 27 2023 Name Medina Shehu Hour 9 50 Solve the problem below by writing and solving an equation Be sure to define your variable There are a total of 122 countries in Africa Europe and North America as of 2012 Europe has twice as many countries as North America and Africa has seven more than Europe How many countries are in each of these three continents Write an equation and solve it to answer this question 9 51 Solve each of the following inequalities for the given variable Represent your solutions on a number line 9 t 23 a 2 3p 1 4 a 2k k 6 0 b 9k 2 3k 10 9 52 Solve the following quadratic equations Check your solutions if possible c 11 21 8 24 c 5 h 4 b m 9 d 3n 4n 5

32 What value of a would make the graph of f x ax open facing up A 8 B 0 C 1 2 33 How can the graph of g x x 4 be obtained from the graph of f x x RESSO 34 35 A By translating f x left 4 units C By translating f x right 4 units A Maximum 1 C Maximum 1 Does f x 3x 6x 4 have a maximum or minimum Find the value B By translating f x up 4 units D By translating f x down 4 units A y 3x 5 B y 2 x 3 5 D 8 B Minimum 1 D Minimum 1 Which quadratic function has a vertex of 3 5 a C y 5 x 5 3 D y x 3 5

36 The graph of y f x is shown Use the graph to identify the factors of f x MARK ALL POSSIBLE ANSWERS A C x 4 x 4 8 A 4 35 8 0 B D 37 Find the coordinates of the vertex for y x 4x 3 B 4 3 x 3 pool on 1 suerbeng guidger x 3 gsig sitt sor C 2 15 10g to gang of D 2 1

30 Solve for x x 10x 24 A x 12 or x 2 C x 12 or x 2 31 Solve 2x 7x 15 0 A x x 5 C x 1 x 5 B x 6 or x 4 D x 6 B x 2 3 D x N W or x 4 2 x 5 x 5

23 Factor completely 2x 14x 10 A 2 x 14x 10 24 Factor completely 9x2 12x 4 A 3x 2 B 2 x 7x 5 A 3a 8 a 6 25 Factor completely 3a 24a 48 26 Solve 3 y 4 0 A y 3 y 4 B 3x 4 3x 1 B 3a 12 a 4 B y 3 y 4 C 2x x 7x 5 C 9x 4 x 1 C 3 a 4 D 2x x 7 5 C y 3 y 4 D 9x 12x 4 D 3 a 8 NOS MARQsne sus du sill einni D y 3 y 4

27 Solve for x A x 2 C x 28 Solve for x A x 6 29 Solve for x A x 3 3x 2 x 4 0 or x 4 or x 4 x 6x 0 B x 6 or x 6 x 6x 9 0 B x 3 B x or x 4 D x 2 or x 4 548 C x 6 or x 0 C x 3 or x 3 D x 0 or x D No solution

19 Which is a factor of the trinomial x2 6x 27 A x 19 A x 3 B x 9 20 One of the factors of x 11x 24 is 0 B x 3 21 Which quadratic function has zeros of 4 and 7 A f x 3 x 4 x 7 C f x 3 x 4 x 7 A 3x 4 3x 4 22 Factor completely 9x 16 C x 9 B 3x 4 3x 4 C x 4 D x 3 D x 4 B f x 2x 4 x 7 D f x x 3x 28 C 3x 8 3x 2 IA D Not factorable

11 Simplify 9n 5 2n 6n 3 A 11n 8 12 Simplify 4x 2x 8 x 3x 2 A 3x x 6 B 11n 6n 8 A 10 13 What is the degree of the following polynomial 3x x5 2x 6 0 B 3x x 10 A 3 B 3 C 11n 6n 8 B 6 C 3x 5x 6 14 What is the leading coefficient of the following polynomial 3x x5 2x 6 C 5 18 D 11n 6n 8 D 3x 5x 10 D 6

Rita is solving this absolute value inequality using a graph 2x 1 4 1 She graphs the following in Desmos y 2x 1 4 y 1 Here is her graph 5 Ox 5 or x 1 O 2 x 1 This image cannot be easily described If you need an explanation of this image please ask your teache for help Using the graph what is the solution to the absolute value inequality 5 x 1 0 x 2 or x 1 5 5

Simplify 12a 5a b 4b 9 A 240a4 b6 B 240a4 b5 A 811 4 Which expression is not equivalent to the others C 1la b B 3 18164 gange D 240a4 b5 HOUS pilo citie C 9 D 3 27 10 In 2012 200 000 people attended the county fair The attendance increases by 8 per year WH function represents the attendance t years after 2012 y 200 000 1 8 y 200 000 0 92 C y 200 000 1 08 y 200 000 1 8

1 2 Which expression is not equivalent to the others A vd esasomoni Which expression is equivalent to x x A x x B x3 x4 3 Simplify A 2x4 B x x 5x 10x7 in the equation to 1 B 4 2x4 0 C x 5 C x x C 1 5x4 D x200 D x x D

4 Simplify 4u v A 12u v 5 Simplify 2 A 8 6 Simplify 7 A 0 B 12u vo B B 1 C 64u v C 6 C 7 8 1 x645 the D 64u4 v6 D 117 D

Solve and graph the answer on a number line 5 1 2 16 O O 2 6 3 3 2 6 2 6 2 6 2 6 2 6

Aspyn wants to solve the equation x 3 1 by using a graph She graphs the following equations in Desmos y x 3 y 1 The graph below is what she sees 5 O No Solution O x 3 0 x 3 x 0 5 10 This image cannot be easily described If you need an explanation of this image please ask your teacher for help According to Aspyn s graph what are the solutions to the equation 5 10

Solve and graph the answer on a number line 3x 1 12 O O O 5 3 3 5 3 3 3 3

The average number of jelly beans in a package is 120 The number of jelly beans can vary by up to 6 Select the absolute value equation that would give you the smallest and largest possible number of jelly beans in a package Ox 120 6 Ox 6 120 O x 120 O 120 6 X 6

y 4 x 1 7 y 5 The graph below is what she sees 5 O x 5 x 7 O x 0 75 x 2 75 LO This image cannot be easily described If you need an explanation of this image please ask your tea for help According to Payton s graph what are the solutions to the equation No Solution 0 5

Select the number line that represents the solution to this equation x 3 2 2 2 3 3 5 5 65

Find the inverse f x for x 4x O f x 4x 3 f x x 3 Of x x 3 O f x 4x 3 12

Which of the following equations shows the transformation of the graph as it relates to the parent graph f x x 10 6 4 2 12 10 8 4 2 2 4 6 8 2 4 6 8 10 Of x x 1 3 O f x x 1 3 O f x x 1 3 O f x x 1 3 CO st N

f x g x 5x 11x 17x 3 x 10x 3 O 5x 10x 15x 3 x 10x 3 Question 12 O Given g x 5x 10x 15 and h x 5 find g x h x O x 2x 10 x 2x 3 2x 3

Of g x x the functions are inverses of each other O f g x x 12 the functions are not inverses of each other Of g x x 6 the functions are not inverses of each other O f g x x 4 the functions are not inverses of each other Question 16 Find the inverse f x for f x x 1 Of x x 3 Of x x 3 2 O f x 3 X 23 3 2