Quadratic equations Questions and Answers

Connor invested 63 500 in 2017 When the investment ended in 2023 he had 71 231 What annual interest rate compounded semi annually did he invest his money at 1 9 0 096 1 0096 0 019

a Use a graphing utility to graph f x x 2x 3 on the interval 2 2 and approximate any local maxima and local minima b Determine where f is increasing and where it is decreasing a Using a graphing utility graph the function for 2 x 2 and 4 y 10 Choose the correct graph below A and it occurs at x The local maximum is y Round to two decimal places The local minimum is y and it occurs at x Round to two decimal places OB O C OU

Solve the equation where 0 x 360 Round approximate solutions to the nearest tenth of a degree 2 sinx cos x 3 sin x 2 cos x 1 0

The graph shows the function g x 6 12 10 8 6 4 2 4 2 0 2 2020 StrongMind Created using GeoGebra 4 13 3 5 2 1 4 1 1 0 2 6 g x 8 10 What is the average rate of change for the function g x over the interval 0 x 4 Enter your answer as a number like this 42

A nature conservation organization tracks the population of an endangered species of foxes over time The population number is modeled by the function f x 1 20 7 10 000 where a represents the time in years since the organization began tracking the foxes Calculate the average rate of change for the population over the following intervals 0 10 20 30 40 50 60 70 Over which time interval did the population decline the fastest GeoGebra Graphing Calculator O 20 30 O 0 10 O 40 50 60 70

The graph to the right is a complete graph that is it is continuous and displays the functions and behavior All zeros are integers Answer the following questions Is the multiplicity of this zero even or odd odd even What is the value of the largest zero x 5 Type an integer or a simplified fraction Is the multiplicity of this zero even or odd even odd What is the value of the other zero x 3 Type an integer or a simplified fraction Is the multiplicity of this zero even or odd odd even 10 10 1 by 100 100 10 m SOU b Write an equation expressed as the product of factors of a polynomial that the graph might represent Use a leading coefficient of 1 or 1 and make the degree of f as small an What is an equation for a polynomial that the graph might represent using the above constraints

f x x x 2 x OD The graph rises to the left and falls to the right b Find the x intercepts State whether the graph crosses the x axis or touches the x axis and turns around at each intercept What is are the x intercept s x 0 2 6 Use a comma to separate answers as needed What does the graph do at x 0 The graph crosses the x axis The graph touches the x axis and turns around What does the graph do at the rightmost zero The graph crosses the x axis The graph touches the x axis and turns around What does the graph do at the leftmost zero The graph crosses the x axis The graph touches the x axis and turns around c Find the y intercept y 0 d Determine whether the graph has y axis symmetry origin symmetry or neither O O SICE Y axis symmetry Origin symmetry Neither

32 Let F be a field and let p x a x a x a x E F x where p x is irreducible over F If p x a x a x a x show that p x divides some a x This exercise is referred to in the proof of Theorem 17 6

On dividing 3x x 2 by a polynomial g x the quotient and remainder were x 2 and 2x 4 respectively Find g x

f x x 4x x 4 below a Use the leading coefficient test to determine the graph s end behavior Which statement describes the behavior at the ends of f x x 4x X 4 A The graph falls to the left and to the right B The graph falls to the left and rises to the right C The graph rises to the left and falls to the right The graph rises to the left and to the right b Find the x intercepts State whether the graph crosses the x axis or touches the x axis and turns around at each intercept What are the x intercepts X Type an integer or a decimal Use a comma to separate answers as needed

following steps to graph the polynomial function f x f x x x 2 x 6 a Use the leading coefficient test to determine the graph s end behavior What does the graph off look like A The graph rises to the left and to the right OB The graph falls to the left and to the right C The graph falls to the left and rises to the right D The graph rises to the left and falls to the right b Find the x intercepts State whether the graph crosses the x axis or touches the x axis and turns around at each intercept What is are the x intercept s x 0 2 6 Use a comma to separate answers as needed What does the graph do at x 0 The graph crosses the x axis The graph touches the x axis and turns around What does the graph do at the rightmost zero O The graph crosses the x axis O COLL The graph touches the x axis and turns around

For the polynomial function f x 2x 6x answer the parts a through e a Use the Leading Coefficient Test to determine the graph s end behavior A The graph of f x falls to the left and falls to the right B The graph of f x rises to the left and falls to the right C The graph of f x rises to the left and rises to the right D The graph of f x falls to the left and rises to the right U L b Find the x intercepts State whether the graph crosses the x axis or touches the x axis and turns around at each intercept The x intercept s is are 0 3 Type an integer or a decimal Use a comma to separate answers as needed Type each answer only once At which x intercept s does the graph cross the x axis Select the correct choice below and if necessary fill in the answer box to complete your choice A The x intercept s at which the graph crosses the x axis is are 0 3 Type an integer or a decimal Use a comma to separate answers as needed Type each answer only once OB There are no x intercepts at which the graph crosses the x axis At which x intercept s does the graph touch the x axis and turn around Select the correct choice below and if necessary fill in the answer box to complete your choice OA The x intercept s at which the graph touches the x axis and turns around is are Type an integer or a decimal Use a comma to separate answers as needed Type each answer only once OB There are no x intercepts at which the graph touches the x axis and turns around

ind the zeros for the polynomial function and give the multiplicity for each zero State whether the graph crosses the x axis or touches the x axis and turns around at each zero f x 9 x 5 x 7 The zeros are 5 7 Use a comma to separate answers as needed The multiplicity of 5 is

ite a polynomial function that imitates the end behavior of the graph shown to the right The dashed portion of the graph indicates that you should focus only imitating the left and right behavior of the graph and can be flexible about what occurs between the left and right ends Which of the following polynomial functions imitates the end behavior of the graph shown above Of x 10x5 2x 2 Of x 8x 5x 4 Of x 3x5 2x 10 Of x 9x 3x 2 CCC

Use the following steps to graph the polynomial function f x f x x x 2 x 6 a Use the leading coefficient test to determine the graph s end behavior What does the graph of flook like A The graph rises to the left and to the right B The graph falls to the left and to the right C The graph falls to the left and rises to the right D The graph rises to the left and falls to the right

For the polynomial function f x 2x 6x3 answer the parts a through e a Use the Leading Coefficient Test to determine the graph s end behavior A The graph of f x falls to the left and falls to the right B The graph of f x rises to the left and falls to the right C The graph of f x rises to the left and rises to the right D The graph of f x falls to the left and rises to the right b Find the x intercepts State whether the graph crosses the x axis or touches the x axis and turns around at each intercept The x intercept s is are Type an integer or a decimal Use a comma to separate answers as needed Type each answer only once

Fill in the blanks correctly complete the sentence below The graph of y 7 4 cos is obtained by shifting the graph y cos r REMOVED THIS ANSWER BOX FOR EXAM unit s horizontally to the Choose C units s vertically Choose It Jse exact simplified values only stretching it vertically by a factor of

For f x x and g x x 1 find the following functions a fog x b g of x c fog 2 d gof 2 a fog x Simplify your answer

2 5 Given f x 3 and g x first find f g f g fg and Then determine the domain for each func g X 7 f g x 3 Simplify your answer What is the domain of f g Type your answer in interval notation

Compare the function rule f x 2 3 and the graph of g x 2 8 6 4 2 0 2 2020 StrongMind Created using GeoGebra 2 4 g x 6 8 Which statement is true about f x and g x and their rates of change for the interval 0 x 3 The rate of change is not defined for g x over the given interval O The rate of change for f x is the same as the rate of change for g x O The rate of change for f x is faster than the rate of change for g x O The rate of change for f x is slower than the rate of change for g x

Q5 Find the average rate of change over the interval 0 x 1 g x x 01 0 2 0 1 2 2 3 1 2 3 4 5 MathBits com X

Q2 To find the average rate of change over an interval use all but which of the following Oslope formula O change in y change in x Orise run O change in x change in y

Consider selecting four elements say a b c and d from the set A a b c d e List all possible subsets of A using all four elements Remember to use set builder notation i e a b c d e X How many arrangements are there arrangements Entor an exact number

Grace is riding her bike to the store from her house following a straight bike path After 10 minutes Grace is 4 miles from her home After 15 minutes Grace is 6 miles from her home What is her rate in miles per minute O2 miles per minute Omiles per minute Omiles per minute

le function f x 4 log x 2 Which interval has the smallest average rate of change in the given function GeoGebra Graphing Calculator 05 x 7 O 1 x 1 03 x 5 1 x 3

Find all the square roots of the complex number 3 3i Write the square roots in polar re form with the smaller angle first Give your angles in degrees Root 1 Root 2 Write the square roots in a bi form with the smaller angle first Root 1 Root 2

2 You are going to send a probe to explore a shipwreck in the ocean The probe will not work when the temperature is below 0 5 C The temperature varies inversely with depth at depths greater than 900 meters At a depth of 3700 meters the temperature is 1 2 C a Create an equation to model temperature Which type of equation will you create b What is the constant of variation c If the depth is 5000 meters what is the temperature d If the temperature is 2 7 C what is the depth e How deep can the probe go before it won t work

Find functions and g such that F fo g Use non identity functions for f x and g x F x 6x x f x x2 Need Help Submit Answer 1 1 Points SCALCET9 1 3 048 Find functions and g such that G Fog Use non identity functions for ftx and g x x g x 06 wwich DETAILS

Use the intermediate value theorem to show that the polynomial has a real zero between the given integers 3 f x x 2x 4 between 1 and 7 Find the value of f 1 f 1 5 Find the value of f 7 f 7

Given f x 8x and g x 3x 1 find the following expressions a fog 4 b gof 2 c fof 1 d gog 0 a fog 4 b gof 2 c f o f 1 d gog 0 Simplify your answer Simplify your answer Simplify your answer Simplify your answer

Solve the following equation with 0 a 2 3 sin a 3 4 Enter your answers in increasing order Round your answers to two decimal places i a 11 AU PA i radians radians radians radians

Find the moduli of the 5 roots of the polynomial p 2 25 5 2 3z 1 and enter a decimal approximation to the largest modulus in the box below Your approximation should be corre at least 10 significant figures

Use the change of base theorem to find each logarithm log 77 log 77 Simplify your answer Do not round until the final answer Then round to four decir

7 Given a and are acute angles with cos a 3 33 5 a sin a b cos a B 5 12 and cot f 7 find c tan a

Solve the equation e8x 1 6 x The solution set is Use a comma to separate answers as ne

Describe the transformations that were applied to the parent function f x in order to create a transformed function g x f x x g x x 3 2 horizontally stretched by factor of 4 3 horizontally translated 3 units to the left and vertically translated 2 units down horizontally stretched by factor of 3 4 horizontally translated 3 units to the left and vertically translated 2 units down horizontally stretched by factor of 3 horizontally translated 4 3 units to the left and vertically translated 2 units down none of the above

a Find the inverse of f b State the domain and range of f c State the domain and range of f 1 d Graph f f1 and y x on the same set of axes a What is the inverse of f Simplify your answer Use integers or fractions for any numbers in the expression b State the domain and range of f Select the correct choice below and fill in any answer boxes within your choice O A The domain off is x The range of f is y Simplify your answers Type an inequality or a compound inequality OB The domain of f is all real numbers The range of f is yl Simplify your answer Type an inequality or a compound inequality OC The domain of f is x The range of f is all real numbers Simplify your answer Type an inequality or a compound inequality OD The domain and range of f are all real numbers c State the domain and range of f1 Select the correct choice below and fill in any answer boxes within your choice OA The domain of f 1 is x The range of f1 is yll Simplify your answers Type an inequality or a compound inequality OB The domain of f1 is all real numbers The range of f1 is y Simplify your answer Type an inequality or a compound inequality OC The domain off 1 is x The range of f1 is all real numbers Simplify your answer Type an inequality or a compound inequality OD The domain and range of f1 are all real numbers d Graph f f1 and y x on the same set of axes Choose the correct graph below O A B O C O D

Find the value In In 81 21 81 21 0 Round the final answer to four decimal places as needed Round all intermediate to four decimal pla

Solve the logarithmic equation Express all solutions in exact form log 2 x 5 x 2 3 Select the correct choice below and if necessary fill in the answer box to complete you choice OA The solution set is Type an exact solution using radicals as needed Use a comma to separate answers as needed OB The solution is the empty set

S lve the system 2x 4y z 6 3x 2y 5z 14 7x 6y 2z 13 C The solution set is 00 Type an integer or a simplified fraction

Solve the system If the system has infinitely many solutions write the solution set with z arbitrary 5x 2y z 0 x y 0 20x 8y 4z 0 Select the correct choice below and if necessary fill in the answer boxes to complete your choice O A There is one solution The solution set is Simplify your answers OB There are infinitely many solutions The solution set is z where z is any real number Simplify your answers Type expressions using z as the variable OC The system is inconsistent The solution set is

Solve the system 3x 6y z 5 3x 3y 5z 12 9x 9y2z 13 The solution set is ID

Solve the system by substitution 2x 8y 16 33 7y 3x The solution set is Type an ordered pair

1 point Find a basis p x q x for the kernel of the linear transformation L P3 x R defined by L f x f 7 f 1 where P3 x is the vector space of polynomials in x with degree less than 3 x 2 1 q x X 2 14x 15 p x

ng answer if correct answer is given i will leave a thumbs up Thank you c Write the expression as an algebraic expression in x for x 0 6 tan arccos x

Find the volume of this sphere Use 3 for TT V ft 18 ft V Tr Hint The radius r is 1 2 of the diameter

Find the volume of this sphere Use 3 for TT V cm V r 5 cm

What will a 120 000 house cost 5 years from now if the price appreciation for homes over that period averages 6 compounded annually The future cost of the house will be Do not round until the final answer Then round to the nearest cent as needed

AREA What is the radius of this circle hm T 70 What is the AREA of this CIRCLE Acircle Thm MINOR SECTOR AREA What is the measure of the angle of the MINOR SECTOR 3 What is the AREA of the MINOR SECTOR AMinor sector Thm MAJOR SECTOR AREA What is the measure of the angle of the MAJOR SECTOR 3 O O What is the AREA of the MAJOR SECTOR AMaior sector Thm

Graph the solution set of each system of inequalitie a x y 4 x y 5 4x y 4 J x