Quadratic equations Questions and Answers

The height H x in meters of an object after x seconds is approximated by the following equation A negative height means the object is below sea lev H x 8x 33x 33 4x 16x 17 Complete the following a Use the ALEKS graphing calculator to find the value of x that minimizes the height Then give the minimum height Round your answers to the nearest hundredth Value of x that minimizes height seconds Minimum height meters b Complete the following sentence For very large x the height appears to Choose one

The concentration of a drug in a patient s bloodstream after t hours is modeled by the formula C t 11 0 74 where C is measured in milligram per liter a What is the initial concentration of the drug b How long does it take for the concentration to decrease to 70 of its initial level a The initial concentration of the drug is milligrams per liter CLER

Given g x ex evaluate each of the following a g In 5 b g In 4 c a in 27 g In a g ln 5 Simplify your answer

Write an equation for the inverse function of the one to one function given f x log 21x Simplify your answer

Vrite an equation for the inverse function of the one to one function given f x gx f1 x

The exponential growth of the deer population in the country can be calculated using the model T 40 000 1 06 where 40 000 is the initial deer population and 06 is the rate of growth T is the total population after n years have passed a Predict the total population after 3 yr The total population after 3 yr is about Round to the nearest thousand as needed

Consider the following Quadratic Function f x 6x 8x 9 State the coefficients of the quadratic in general form a Number b Number C Number

Solve the given logarithmic equation 1 log x 25 2 The solution set is

Find the future value and interest earned if 8706 54 is invested for 8 years at 6 compounded a semiannually and b continuously a The future value when interest is compounded semiannually is approximately Type an integer or decimal rounded to the nearest hundredth as needed

Assume that the radius r of a sphere is expanding at a rate of 11in min The volume of a sphere is V f Determine the rate at which the volume is changing with respect to time when r 5in The volume is changing at a rate of in min

Check all that apply 11 Describe the transformations on y f x that have taken place to produce y 3f x 2 5 Flipped upside down Moved 2 units to the right Moved 2 units to the left Moved up 5 units Moved down 5 units Less steep wider More narrow thinner

the sum of a number q and sixty four divided by eighty three

Write the equation for the graph shown below The parent function is f x x shown as a dotted graph Equation a f x x 6 O A OD b f x x 6 17 c f x x 6 d f x 6x

Which of the following is true for the parent function of square root functions CHOOSE ALL THAT APPLY A Domain of All Real Numbers Domain of x 0 C Range of All Real Numbers D Range of y 20 Contains the point 0 0 E A B E B F Contains the point 1 1

In problems 6 and 7 determine which parent function best describes the situation 6 You have a lemonade stand on the side of the road A car drives at a constant speed down the road toward your stand and then away from your stand as it passes O A B C D A A Linear B B Quadratic 7 A ball is thrown up in the air from a starting height of 6 feet and lands on the ground 8 seconds later A Linear C Square Root B Quadratic D Absolute Value C Square Root D Absolute Value

Use a graphing utility and the change of base property to graph the function y log 11x SLIKA Use the change of base property to rewrite the given expression in terms of natural logarithms or common logarit log 11x

1 point Find all solutions of the equation 2 cos x 1 0 The answer is A Bk and C Dk where k is any integer 0 A 2 B A C D

Each letter of the alphabet is assigned a numerical value according to its position in the alphabet The function defined by f x 2x 3 was used to encode the following message 1 25 5 33 7 43 Find the inverse function and determine the message The inverse function is 13 1 35 1 33 33 15 41 7 5 f x Use integers or fractions for any numbers in the expression

The graph of a function f is given Use the horizontal line test to determine whether f is one to one B

Solve the equation 3 7 9x got is

Solve the equation x5 3 32 The solution set is Use a comma to separate answers as nee

Determine if the function f x x 3 x 2 is one to one If so find the inverse Graph f X 2 and f on the same axes Give the domain and the range off and f1 If f x is not one to one say so Write an equation for the inverse function Select the correct choice below and if necessary fill in any answer boxes to complete your choice What is the inverse of f x OA The function f x is one to one and f x OB The function is not one to one Simplify your answer

Determine whether the function is one to one If so a write an equation for the inverse function in the form y f x b graph f and f1 on the same axes and c give the domain and the range of f and f1 If the function is not one to one say so f x x 4 a Write an equation for the inverse function in the form y f x Select the correct choice below and if necessary fill in any answer boxes to complete your choice O A The function f x is one to one and f x Simplify your answer OB The function is not one to one

For the function on the right determine whether the function is one to one Domain 20 Hours 30 Hours 45 Hours 75 Hours Range 100 200 250 275

Drag the movable red point to shift the function the black point to set the vertical asymptotes and the blue point at the correct set of coordinates You may click on a point to verify its coordinates Note Make sure to move the points in the direction of the phase shift represented in the function Provide your answer below A 3T 21 30 8 7 6 5 4 3 y csc 1 x 7 1 02 2T 3TT

1 For f x 5x 8 and g x x 8 find fog x and gof x Then determine whether fog x gof x What is fog x fog x What is g o f x gof x Does fo g x gof x O Yes O No

Give the equation of the function graph below 4 3 2 18 9 8 7 6 5 4 3 1 2 4

12 Let A represent f x If B is a transformation of A identify the equation of B 10 5 0 5 10 10 5 A y 0 B 5 10 X Equation of B

ting Given the graph of the function f x below sketch the graph of f x 2 4 7 3 1 5 X 6 6 3 4 y

For 1 sketch each of the indicated parent functions a Quadratic H d Square Root mok b Absolute Value 1 what e Exponential Growth c Cubic H f Linear V noisin

7 The following graphs have been transformed from their parent functions Write the equations of the new graphs a Parent Function f x x Equation b Parent Function f x x Equation etibesa E

ne 5 The function f x has a domain of x 3 and a range of y 2 Determine the domain and range it function is transformed to the function below a f x 3 2 Domain Range b f x 4 Domain Range 018 Istingnoqx C f x 6 Domain Range JODA 916Up2

2 What is the domain and range for the function graphed below 5 2 1 3 2 1 0 1 2 1 2 3 4 5 Domain Range S

The polynomial of degree 5 P x has leading coefficient 1 has roots of multiplicity 2 at x 2 and X 0 and a root of multiplicity 1 at x 1 Find a possible formula for P x P x

Determine the possible number of pos f x 2x 4 18x 2 7x 12

Solve the equation r 2 r 11 0 Fully simplify all answers including non real solutions

Write an equation for each circle Each interval represents one unit

16 Jeffrey s company has been operating for 45 months In the beginning Jeffrey was seeing incredible profit growth every month As more companies started to adjust their services to compete with Jeffrey s business Jeffrey s profits leveled out and have started to fall off Jeffrey s business life cycle can be modeled by the equation p 1 2m 0 02m where p is the profit of his company in millions and m is the number of months since his business started Graph this situation on your calculator or on a sheet of paper What is the reasonable domain during this company s profitability OD 0 m 60 OD 0 m 45 OD 0 p 64 OD 0 p 70

When is cluster sampling appropriate Select the correct answer below Cluster sampling is a good choice when the population has multiple distinct groups that are each likely to be representative of the population as a whole Cluster sampling is a good choice when the population has multiple distinct groups that are internally homogenou but not representative of the population as a whole Cluster sampling is useful if the population is not well understood or there are no groups within the population tha need to be analyzed individually Cluster sampling is a useful method when the individuals in the population are generated in a continuous stream like on an assembly line

1 High salt intake is a leading cause of high blood pressure Canadians consume an average of 8750 mg of salt about 6 tsp per day the recommended maximum is 5750 mg In a recent study of people with high blood pressure patients salt intake was reduced for one month and the change in blood pressure was recorded c d SALT REDU 1 CTIO N 4 8 5 1 BLOOD PRESSURE 3 2 6 3 4 9 4 0 7 8 4 5 8 1 5 3 2 7 3 6 5 1 4 4 6 3 a State the independent and dependent variables REDUCTION mmHg 5 3 6 1 3 5 7 2 4 4 5 1 9 8 5 0 12 5 5 0 2 7 4 1 5 9 4 6 7 1 INDEPENDENT DEPENDENT Describe the relationship between the two variables Complete the table below to 2 decimal places r VALUE TYPE OF CORRELATION EQUATION OF LINE OF BEST FIT e How well does the line fit the data EXPLAIN USE THE EQUATION If Victoria lowered her salt intake by 5 0 g what change

sample appropriate Select the correct answer below A simple random sample should always be used if possible A simple random sample should be used if the population is not well understood or there are no groups within t population that need to be analyzed individually A simple random sample should be used when the population has well defined groups that are relatively homogeneous This will make sure each group is represented proportionally

The average emergency room cares for 300 patients each day There are 20 nurses on duty in the emergency room each day and they share the patient load equally Suppose one patient is chosen at random Identify the numbers of each of the following and enter the probability as a simplified fraction Provide your answer below There are There are P N patients in the sample space nurses on duty each day is the probability that a patient will be assigned to a specific nurse

A town planner is interested in getting some demographic data about the households in the city The city has four wards with the following numbers of households ward A has 2 107 ward B has 903 ward C has 1 505 and ward D has 1 499 The budget for the project allows the planner to survey 100 households She plans to use a stratified sampling method What number of households should be chosen from ward B Enter a whole number Provide your answer below

The pH of a chemical solution is given by the formula pH log 0 H where H is the concentration hydrogen ions in moles per liter Values of pH range from 0 acidic to 14 alkaline Answer parts a through pH 4 p an integer or a decimal c What is the pH of a solution for which H is 0 00001 pH 5 Type an integer or a decimal d What happens to pH as the hydrogen ion concentration decreases pH increases pH decreases e Determine the hydrogen ion concentration of a solution with pH 3 9 H M Round to six decimal places as needed

Solve and check the equation Points 5 10 2x7 2 4 0

If a single pane of glass obliterates 4 of the light passing through it the percent p of light that passes through n successive panes is given approximately by the function below p n 100 0 96 a What percent of light will pass through 10 panes b What percent of light will pass through 25 panes c Explain the meaning of the base 0 96 in this problem a The percent of light that will pass through 10 panes is approximately Round to the nearest whole number as needed

Find the hydrogen ion concentration for Lemon Juice with a pH of 2 0 Hint pH moles per liter help numbers log H

Suppose that g x 7 6 a What is g 1 When x 1 what is the point on the graph of g b If g x 349 what is x When g x 349 what is the point on the graph o a g 1 The point is on the graph of g Type integers or simplified fractions

Solve the system by substitution 2y 5x 4 x y 2 2 The solution is Simplify your answer Type an ordered pair

4 If limx a g x M where M 0 show that there exists number 0 such that 0 x a 8 g x IM 2