Quadratic equations Questions and Answers

1 Find the domain of the following functions a x ln b g x 3x3x 3x 1 1 x d 1 1 x log3 1 2x x c h x log log log x k x log 5 x

The table gives a set of outcomes and their probabilities Let A be the event the outcome is less than 3 Let B be the event the outcome is prime Find P AIB Outcome Probability 1 0 2 0 2 0 2 0 4 23 4

5 6 4 Dave has a savings account that pays interest at 31 per year His opening balance for May was 1374 67 He did not deposit or withdraw money during the month The interest is calculated daily How much did the account earn in May received 93

Of the cones recently sold by an ice cream shop 47 had pistachio ice cream and 51 had oth flavors What is the experimental probability that the next cone sold will have pistachio ice cream Simplify your answer and write it as a fraction or whole number P pistachio

Select all expressions that are squares of linea expressions 2 X 12x 36 2x 5 2 x 49 x 7 x 7 x 100 2 2 x 14x 49 Select all that apply

1 Solve this equation by completing the square Show your reasoning you may use the sketch space below OR use notebook paper take a picture and upload it into the textbox x 12x 20 4 2 Solve this equation by the factoring method setting the equation equal to zero rewriting it into factored form and using the Zero Product Property Show your reasoning you may use the sketch space below OR use notebook paper take a picture and upload it into the textbox 2 9x 12x 5 10

Consider the functions f x x 7 and g x 4x What is f x g x f x g x 4x x 7 f x g x 4x x f x g x 4x x 7 O f x g x x x

2 Select all equations that are equivalent to x 6x 16 Select all that apply x 6x 9 0 x 6x 9 16 x 6x 9 25 x 3 0 x 3 16 x 3 25

A solution to an equation Jada solved is 2 3 She is trying to determine whether that solution is rational or irrational Jada knows that 2 is a rational number and 3 is an irrational number She also knows that the sum of any two rational numbers is always rational 1 If we add 2 to 2 3 what is the sum Is the sum rational or irrational the number 2 is a rational number 2 Explain why 2 3 cannot be rational HO

Solve the equation 4x 5x6 0 using any algebraic method Show your reasoning tf

A quadratic function is defined by f x x 8x 4 Which expression also defines f and best reveals the maximum or minimum of the function x 4 20 Ox x 8 4 x 4 12 x 4 20

6 4 2 8 6 4 2 0 2 4 6 8 A 2 4 6 8 2018 StrongMind Created using GeoGebra Which statements are true Select all that apply O The function is increasing over the interval 8 x 2 The function is decreasing over the interval 3 x 7 The function is constant over the interval 2 x 2 O The function is increasing over the interval 2 x 3 The function is increasing over the interval

B Side c Angle A b Note Triangle may not be drawn to scale Suppose a 15 and b 8 Give the value of each of the following Give answers as integers a rounded to 2 decimal places as appropriate Angle B C A degrees degrees

For the following function determine the exact amplitude and find the phase shift in radians y 6 sin x cos x The amplitude is JOL BE ing radionic as pooded

the pair of similar figures find the missing area Round your answer to the nearest tenth if necessary 8 5 in in A 34 in 2 in A

A manufacturer has two sites A and B at which it can produce a product and because of certain conditions site A must produce three times as many units as site B The total cost of producing the units is given by the function C x y 0 5x 100x 660y 130000 where a represents the number of units produced at site A and y represents the number of units produced at site B Round all answers to 2 decimal places How many units should be produced at each site to minimize the cost units at site A and at site B What is the minimal cost What s the value of the Lagrange multiplier

From a boat on the lake the angle of elevation to the top of a cliff is 21 20 If the base of the cliff is 749 feet from the b how high is the cliff to the nearest foot a 303 ft b 293 ft c 306 ft d 296 ft 21 20 749

A man and a woman standing 2 miles apart spot a 2 hot air balloon directly between the two of them If the angle of elevation from the man to the balloon is 29 and the angle of elevation from the woman to the balloon is 42 find the altitude of the balloon to the nearest foot

f in a right triangle 0 18 and the side adjacent to has length 7 how long is the hypotenuse Round to at least 3 decimal places

The volume of a square based prism is V x h x is the length of a side of the base and h is the height What are the dimensions of the prism with largest volume if the sum of the length of one side of the base and the height is 4

graph below Which function represents the dotted graph 10 9 8 7 6 5 4 3 2 1 Y X 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Oy f x 4 2 Oy f x 4 2 Oy f x 4 2 ny f x 4 2

Below is the graph of y log x Translate it to become the graph of y log x 2 3 6 3 X

The function g is defined by the following rule 8 x 11 10 Find g x for each x value in the table X 1 0 1 2 g 0 10 0 0 3 X 08 S

Multiply and simplify 5 6 2 6 For 2 3 you may type 2sqrt 3 For 8 2 3 you may type 8 2sqrt 3 Or click in answer box the Yellow bar to use the Math Quill ALWAYS click PREVIEW button before submitting Do not use a calcu to enter answer as a rounded decimal Write the exact simplified form

The should summarize all the ideas of the essay O body O rebuttal Othesis statement

In the accompanying diagram of right triangle ABC ZA is a right angle AC 8 AB 15 and BC 17 Find the ratios that are represented by the following 12 a tan B b csc C c cot C 15 d cos B 7 e sin B f sec B g sin C 17 h tan C i esc B j sec C k cot B 1 cos C 17 8 8 17 8 15 7 A

Write a quadratic equation in vertex form to represent a function with the following vertex using a leading coefficient other than 1 7 200 600 8 9 10 0 10 0 30

12 h x 4 x 1 5 a Vertex b y intercept c Domain d Range

form of a quadratic function Factored form of a quadratic function Vertex form of a quadratic function Find the vertex of the following quadratic dratic Functions Vertex Form y y y cauer

Opening Activity Which of the following is equivalent to cos 35 1 1 esc 35 cot 35 1 2 1 sin 35 3 1 sec 35

3 Convert each of the following angles given in radians to degrees a b

lumber mills in historic parks A typical water wheel makes 1 complete revolution every 90 seconds A paddle starts its cycle 1 meter below the level of the water and reaches a maximum height of 4 meters above the water Assume that the timing starts when the paddle is at the top of the water wheel A Make a graph that represents the motion of the wheel 42 B What is the amplitude and period of the water wheel C How high is the center of the wheel above the level of the water D What is the equation of this function

N K 65 85 146 48 mi M 64 L miles W 32 mi 65 48 mi X These figures are congruent What is NK V 35 mi

Use the reference points and the asymptote to write the function whose graph is shown 1 2e 3 2 4 y 3 2 0 2 y 2 8 6 2 ty 2 0 2 y 2 4 5 8 6 4 00 8 1 y 12 10 8 6 4 2 4 y 2 2 12 87 1 6 0 2 2 A X 2 13 y 3 6 4 y 12 4 0

From Kensington how much farther is it to Salem than to Norwood Use the paths shown Norwood mi Kensington 9 1 mi Rockport mi mi Salem Write your answer as a fraction or as a whole or mixed number

Playing with toy alphabet blocks Dani mixes four of the ABCDE blocks into some combination doesn t care about the order Then she takes the XYZ blocks and carefully puts these into a specific order How many different outcomes are possible for this arrangement of seven blocks

Enter an equation for the line of symmetry for the function f x 64x2 64x 16 X

Consider this right triangle 5 8 8 Enter the ratio equivalent to cos 0

10 10 5 5 Parent function f x x 5 10 What is the domain of this function

each expression 4 5 4 3 4 4 44 4 1 1 64 0 1 1 4 0 1 16

6 Does the graph shown represent a function Explain In A The graph represents a function because there is exactly one y value for each x value B The graph does not represent a function because there is exactly one y value for each x value The graph represents a function because some x values have more than one corresponding y value D The graph does not represent a function because some x values have more than one corresponding y value

The first vector is 2 on the X axis and 5 on the Y axis The second vector is 3 on the X axis and 1 on the Y axis What is the final vector Select one O a 5 6 O b 5 4 O C 7 2 O d 6 5 Clear my choice Give the magnitude and direction of the final vector in 9 Select one O a 6 4 38 7 O b 7 8 50 3 O c 38 6 4 O d 7 3 15 9

In 7 what is the direction part of the resultant vector Select one O a 45 5 O b 35 5 O c 9 0 O d 54 5

A ship traveled 50 miles east and 70 miles north What is the distance part of the resultant vector Select one O a 11 miles b 86 miles O c 50 miles O d 7 400 miles

mwent from his home to school by walking 60 yards due east and then yards due north How far is it from his home to the school in a straight ect one a 10 000 yards b 6 400 yards c 100 yards d 10 yards

above what angle from due east would Sam have to walk school from his house by the most direct route one 0 02 1 3 53 1 70

mbination of two vectors is called the one magnitude resultant inverse sine

Use the equations below to help you answer the question A 4X 2Y 3Z 10 B 2X 2Y Z 6 C X 3Y 4Z 22 What is the value of Y that satisfies all three equations Select one O a 2 O b 4 OC 3 O d 3

The maximum number of possible solutions for Y AX B and X y C is Select one O a 2 b 4 O c 3 d 1

2 A 2 X and D 3 What is the value of A D 2 in simplest form Select one O a O b O c O d x 10X 25 4x 20x 100 2x 10X 2 2x2 20X 50