Quadratic equations Questions and Answers

24 Let f x 1 1 What is the point of maximum growth rate for the logistic function f x Round your answer to the nearest hundredth 0 42 3 O 0 85 24 O 0 85 12 0 4

Let f z 11 1 24 1 3e 1z What are the asymptotes of the graph of f x Select each correct answer O y 24 y 0 O y 3 y 1 3

3 Graph the following function f x 2x 7 Instructions Click the graph tab Click on the graph background to add a point Add two points to create a graph Drag a point or type in x and y coordinates to edit its position Click on a point to delete it Graph 1 6 CO 6 6 Co 6 Zoom In Q Zoom Ou Focus

1 f x 2 2 Make and fill in a table of values using 3 random x values You will need to use values near the turn of the graph X y Select Select Select Select

EVALUATE round all answers correctly to three decimal places 1

mine the solution to the system of equations below You must show work for all questions to get credit 1 y 1 y 3x 1 2 8x 4y 16 6x 20 A 0 1 B 1 0 2 8 C 7 1 B 2 1 D 7 1 C 2 1 D 2 1 3 2x 3y 4 y x 4 4 x y 7 6x 2y 18 A 8 1 8 4 B 2 1 D 1 1 A 1 6 C 1 6 5 7x 2y 18 x y 9 6 5x 3y 2 4x y 10 B 1 6 D 2 6 4 5 C 4 1 B 4 1 D 7 4 A 4 6 C 3 6 B 3 6 D 3 6

Work 3x 2y 16 x 3y 10 Substitute 3y 10 equation Distribute muljely 3x 2y 16 3y 10 3y 16 3 3 2x 16 gy ay 16 3 3x 10 ay 16 30 16 7y 30 16 30 v Combine XP Tw Cancel the constant w Concel the coefficien Plug in 2 value ind 2 FG Solve Plug in 2 valle inte 210 Jolye Write as ordered Pair Try It Again Problem Solve the system shown below listing your answer as an ordered pair 3x 2y 14 y 5 2x 3 5 2y 14 315x 27 14 3 3x 2 2y 14 15x 10 2y 14 13y 10 14 10 10

1 Convert the equation from point slope form to slope intercept form y 3 5 x 10 2 In the question below what information are you given What type of line equation can you create with that information Answer the question below and show all of your work What is the equation for a line that passes through the points 4 1 and 8 14 OA y 4 B y x 6 Oc y x 6 O D y 2 4

3 Which ordered pair below is a solution to the system of equations a 1 1 b 2 4 c 1 1 d 4 2 x y 3x 4 y

4 What value for x 2x 7x 4 0 makes the equation true 2x 1 a 6 b 5 c 4 d 3

3 Given the syst Extension Questions 1 Which value for x below is a solution to the equation x 3 x 5 0 a 3 b 5 c 7 d 9 Extend look at the equation What other value of x would make the equation true

S Given the following graph write a possible equation that could represent the function in factored and standard form LA Factored Form Standard Form

For the polynomial function y 3 4 5 2 1 5 match each of its zeros with their multiplicities and their appearance on the graph DRAG DROP THE ANSWER 1 2 3 4 cross cut through bounce wiggle bend Multiplicity Appearance on Graph 2

flights Flying Time 3 hrs 30 min 3 5 5 hrs 20 min 5 33 Fuel Con sumption Per Hour 6 gallons 12 gallons Amount of Fuel 5 gallons 20 gallons 40 gallons 5 gallons Used 1 2 3 4 hrs 4 5 4 4 hrs 22 min 4 375 5 6 hrs 10 min 6 17 6 2 hrs 24 min 2 4 3 hrs 12 min 3 2 7 15 gallons 8 5 hrs 5 min 5 08 18 gallons 9 How much gasoline will be consumed in a flight of three hours forty minutes If the engine uses nine gallons per hour 3 67 x 9 10 An airplane makes a flight of six hours forty two minutes The engine uses an average of 18 gallons of gasoline per hour How much gasoline will be consumed during the flight

14 evaluate at x 2 If needed round correctly to hundre 2 DIGITS PASSED THE DECIMAL Tunc onco

Jeff used the equation 16 3f 1 to calculate how many flowers were growing in his yard How many flowers did Jeff have growing in his yard A B C 4 5 84

Which of these polynomial functions is graphed below O 8 6 4 2 A B C D 60 50 40 30 20 10 2 4 10 201 y x 3 y x 27 y x 27 y x 3 x 6 8

Graph the cube root function and analyze the minimum and maximum on the given interval f x x 4 7 1

14 2x 2y 12 y 3x 12

10 3x 2y y 2x

12 y x 3 3x y 9

16 2x 3y 5 y 2x 1

11 x y 2 y 4x 1

4x 3y 6 y 2x 4 15

Question Solve the system of equations graphed on the coordinate axes below 6 y 3x 7

ve the system of equations graphed on the coordinate axes below 8 6 Y x 3 14 12 3 3 5x 1 2 3 y 3 2x 1 4 5 6 7 8 10 y 1 2x 3

3 In 2005 the Enterprise Southern Maryland News had 37 000 subscriptions The number of subscriptions subsequently decreased by 8 each year Write and use an exponential decay model to find the number of subscriptions in 2024

12 x 4y 4 5x 4y 12 10

Sometimes a quantity is constantly increasing or decreasing at an exponential rate and not just after each year month day hour etc Write the formula to the right which can be used to find the balance of the account in these such cases A r is positive for growth models and negative for decay models

4 In November 26 students at Great Mills High School had contracted the flu Each month the number of students who have contracted the flu increases by 36 Write and use an exponential growth function to find the total number of students who have contracted the flu by May

Evaluate 10m 4 when m 5 and n 4

Evaluate 8r rs when r 6 and s 5

Factoring the Difference of Squares Factor each completely 1 9x 1 3 36k 1 5 2x 18 2 4n 49 4 p 36 6 196n 144

Factoring Trinomials when a 1 11 b 16b 60 13 x 2x 8 15 2x 32x 120 17 6m 36m 42 19 5k 5k 10 12 n 14n 40 14 n 12n 32 16 5n 30n 135 18 2p 6p 140 20 46 40b

Factoring When A does not equal 1 Factor each completely 1 3p 2p 5 3 3n 8n 4 2 2n 3n 9 4 5n 19n 12

The plot below represents the function f x 5 43 2 1 5 4 3 2 1 1 2 5 Evaluate f 1 1 2 3 4 5

4 y 2x 6 y 3x 7

e of the solution to each system 2 y 3x 5 y 4x 7

Where does the graph of the function h z 272 125 cross the z axis B C 2 1 1

3x 9x 12x x 3x 28 HACI R 6 D X

Solve the following equation for x Show all work 32x 27 2x 1 X D BIUS X x Font Size Q A A

2 x 9x 20 9x 12x 4

Question 1 5 Select the pair below which shows the correct conversion from logarithmic form to exponential form O log x 9 and 2 9 log x and 2 92 9x 9 and x 2 O log x O log x 9 and 9 9 and x 9 2x

A certain type of bacteria increases according to the model P t 300e0 75t where t is the time in hours and 300 represents the amount of cells that were originally present Part A Which number in the equation indicates the growth rate 300 e 0 75 time Part B Calculate the approximate number of cells that will be present after 6 hours 300 635 14 000 27 000

16x 16x 3x x 9x 18 2 6x 13x 6

An object is launched off a 215 foot platform If the object was launched at 135 feet per second determine how long it will take for the object to hit the ground ROUND YOUR ANSWER CORRECTLY TO THE NEAREST TENTH Type a response

Which graph represents the function 1 x 2

If f x log4 2x 7 and g x log4 3 find a value for x that satisfies f x g x Use the Numeric Grid to type the solution X 0 00000 0000 0000000 000000 0 00000 2 3 3

2x 3x 2 5x 22x 15 2x 15 Spronks F 22 687 25

Question 1 2 Solve the equation 4 3 2x 6 7 O X O O x 6 O No Solution X 6 8 x