Quadratic equations Questions and Answers

d 1 3 B y 5x 1 D y 5x 8 8 8 through 1 4 and 0 4 A y 4 C y 4x B y 2x D y 4x

11 Write the slope intercept form of the 9 Slope 2 y intercept 1 A y x 2 C y 2x 2 B y 2x 1 D y 2x 2 11 Slope 2 y intercept 2 A y 2x 2 C y 2x 2 B y x 2 D y 2x 2

Order each expression from the least value to the greatest value 12 2 4 8 12 2 4 8 12 2 4 8 START ORDER

26 y cotx Fig 2 6 i Fig 2 6 ii The following table gives the inverse trigonometric function principal value branches along with their domains and ranges Note sin 1 cos cosec sec 1 tan 1 cot 1 MATHEMATICS NCER repub Solution Let sin 2 1 1 1 1 R 1 1 R 1 1 R R Rationalised 2023 24 y Then sin y T T 1 2 2 0 EN EN T T 0 22 0 Y y cotx 1 1 sin x should not be confused with sin x In fact sin x sin x similarly for other trigonometric functions 2 Whenever no branch of an inverse trigonometric functions is mentioned we mean the principal value branch of that function T 3 The value of an inverse trigonometric functions which lies in the range of principal branch is called the principal value of that inverse trigonometric functions We now consider some examples Example 1 Find the principal value of sin 0 and ched

For the function g x solve the following inequality X 9 X 4 g x 0 Select the correct choice below and fill in the answer box within your choice OA The solution is Simplify your answer Use a comma to separate answers as needed OB The solution is Simplify your answer Type your answer in interval notation

2 x 14x 45 0 The solution is Type your answer in interval notation Use integers or fractions for any numbers in the expression Type an exact answer using radicals a

where S is the surface of the garden defined above and n is a unit normal to the surface S Evaluating this surface integral will measure the tendency for the air to circulate in the direction that Anna likes to walk around her garden Note that a negative value just means that she is walking into the breeze Hints An application of Stokes theorem suggests the answers in i and ii should be equal to each ther You may use the integrals sin u du u 2 1 4 sin 2u sinu sin u cos u du 1 4 cos2u Further hints on next page

K JWH payment on a mortgage reduces both the size of the monthly payments and the total interest paid Calculate a the reduction in the monthly payment by increasing the down payment by the amount specified and b the amount saved on interest over the life of the loan Assume the mortgage is for 30 years and use the amortization table to find the monthly payments Increase in Down payment 15 000 Click the icon to view a table of monthly payments on a 1 000 loan Amount of Loan Interest Rate Down Payment 162 000 5 38 000 COLLE a The monthly payment will be reduced by 80 55 when the down payment is increased by 15 000 Round to the nearest cent as needed b Increasing the down payment by 15 000 saved on interest over the life of the loan Round to the nearest cent as needed Monthly Payment on a 1 000 loan Annual Interest Rate 4 5 6 8 10 3 29 53 29 97 30 42 31 34 32 27 Number of Years for the Loan 4 10 22 58 10 12 23 03 10 61 23 49 11 10 24 41 12 13 25 36 13 22 20 6 06 6 60 7 16 8 36 9 65 30 4 77 5 37 6 00 7 34 8 78 X

4000x The polynomial function defined by f x x 10xx can be used to find the depth that a ball 20 cm in diameter sinks in water The constant d is the density of the ball where the density of water is 1 The smallest positive zero of fix equals the depth that the ball sinks Approximate this depth for each material and interpret the results a A wooden ball with d 0 9 b A solid aluminum ball with d 22 e A spherical water balloon with d 1 a Select the correct choice below and fill in any answer boxes in your choice OA The depth is Type an integer or decimal rounded to the nearest hundredth as needed OB The answer is undefined

Consider the min cost max flow problem where we have 6 nodes a b c d e f with supply on nodes b e f Sb 3 se 5 sf and demand on nodes c d 4 Sd The network has 9 arcs a c a d b a b c c e d b e a f b f d with associated costs Sc Cac 0 Cad 6 2 1 Cba 8 Cbc 3 Cce 2 Cdb 5 Cea 2 Cfb 0 Cfd 10

Find the domain and range for the following graphs 2 points each y 51 f 3 2 3 4 5 5 46 Domain Range 00 8 9 10 11 12 X Domain Range 2 1 4 3 2 1 0 2 4 1 2 B

12 5 xvr 1 sinh x Using the trial and error method the value of is obtained x 3 18

Homework 3600 60x Part 1 of 4 Suppose that a parking attendant can wait on 60 cars per hour and that cars arrive randomly at a rate of x cars per hour Then the average number of cars waiting in line can be estimated by N x Complete parts a though c below a Evaluate N 33 and N 59 N 33 0 Round to two decimal places as needed Points 0 of 1

For f x 8 X 4 1 and g x find X a fog x b the domain off og

10 Listen Find the y intercept of the line y 0 16 0 16 12 0 0 0 12 x 12

Parents wish to have 140 000 available for a child s education If the child is now 3 years old how much money must be set aside at 7 compounded semiannually to meet their financial goal when the child is 18 i Click the icon to view some finance formulas The amount that should be set aside is Round up to the nearest dollar

Estimate the one sided limits a lim f x b lim f x for I a x z a 4 x a lim b lim 8 z a 4 x x 4 x and a 4

A BOOK Find the area of the figure 4 in 4 in 4 in 8 in 4 in A in bh Area of atriangle 2 b base h height Area of a rectangle lw length w width t

Next question You can retry this question below Find the equation in terms of 2 of the line through the points 2 5 and 3 2 y 3x 11 Check Answer

Given the points 10 0 and 5 1 find the slope

Next question Find the equation in terms of x of the line through the points 4 1 and 2 3 5 X OF

Give the slope and the y intercept of the line y 8 2x Slope y intercept

Find an equation for the line perpendicular to y Write your answer in the form y mx b y 1 15 9 and goes through the point 3 7

mplify by factoring 90 90 Type an exact answer using ra

Simplify by factoring 90 90 Type an exact answer using ra

POSSIBLE POINTS Compare f x z to the function f 2 x 4 1 Choose the descriptions that describe the change to the parent function Select all th apply A Right 4 B Left 4 C D E Reflected over the x axis Reflected over the y axis Down 1

10 8 6 4 101 Equation 5 5 10 2 6 8 10 Write the equation of the line shown Be sure to use the correct variable

hoose the correct equation to represent this function 5 4 3 2 1 20 H 2 5 A f x x 4 3 B f x 3 4 C f x x 3 4 D x x 4 3

Question 5 nd the equation in terms of a of the line through the points 4 1 and 2 3

Choose the correct graph to represent the function f x x 3 1 A B D 123 54344 1 3 C D 54 1 2 1

Graph the given interval and then express the given interval as an inequality in terms of x 0 1 Choose the correct graph below O A O C 10 10 O A x 1 8 OB x2 1 Choose the correct inequality 6 4 2 1 0 0 2 2 4 st 4 6 6 8 8 10 10 O B 10 10 8 8 6 6 4 N 2 1 0 0 2 2 4 st H 6 6

An approximation for e is given below Use this approximation to round e to the nearest hundredth e 2 718281828459045 The value of e rounded to the nearest hundredth is

Write the decimal 0 32539 rounded to the nearest tenth of a percent 0 32539

Express the given decimal as a percent 0 64

Write the percent as a decimal 220 220

ve by completing the square 2x 3 0 The solution set is Simplify your answer Use a comma to separate answers as needed

Graph the quadratic function f x x 5 2 4 Give the a vertex b axis c domain and d range a The vertex is 5 4 Type an ordered pair Use the graphing tool to graph the function Click to enlarge graph W Click the graph choose a tool in the palette and fol 10 9 8 7 6 5 4 3 2 4 10 9 8 7 6 5 4 3 2 11 2 3 4 AY 6 7 8 9 10 X 10 A C C C Select

Graph the quadratic function f x x 2 Give the a vertex b axis c domain and d range a The vertex is 2 0 Type an ordered pair Use the graphing tool to graph the function Click to enlarge graph Click the graph choose a tool in the palette and fol Ay 10 9 8 7 6 5 4 3 2 4 10 9 8 7 6 5 4 3 2 11 2 3 4 5 6 7 8 9 10 X 5 6 7 8 9 10

ist all potential rational zeros x x 3x 21 Points 0 of 1 Which of the following choices lists all the potentia OA 1 3 OB 7 21 OC 0 1 3 7 21 OD 1 3 7 21

List all possible rational zeros of the function 3 f x 15x 6x 6x 17x 4 Which of the following are the possible rational zeros OA 1 1 3 3 5 5 15 15 24 24 2 4 2 4 OB OC 1 1 3 3 5 5 5 5 15 15 1 3 5 15 5 424242 H 2 1 2 2 2 4 4 4 2 OD 1 1 1 2 351535 1535 15 4 1 1 1 2 2 2 4 4 4 1 2 4 3 5 15 3 5 15 3 5 15

Write the point slope form of the equation of each line given the slope and y intercept 9 Slope 0 y intercept 5 7 A y 5 3x 5 C y 5 0 A y x 5 7 B y 5 x 5 B y 5 3x D y 5 4x 10 10 Slope y intercept 5 C y x 5 5 5 x 5

1 Slope Write the point slope form of the equ slope 1 through 1 0 slope 5 A y x 1 4 B y 1 5x C y 4 x 1 D y 5 x 1 3 through 5 4 slope A y 5 x 4 5 B y 5 x 4 C y 4 x 5 D y 4 5 x 5 6 5

ion of the line through the given point with the given 2 4 2 through 5 5 slope undefined A 0 x 5 B 0 x 5 C y 5 0 D y 5 0 4 through 2 1 slope 3 3 A y 2 x 1 5 B y 1 3 x 2 C y 1 x 2 3 3 D y 2 x 1

1 3 0 5 0 3 Choose the correct polynomial SOA 14 3 45x45 OC f x x 14 3 f x x 5 5 IT OB OD 14 3 x x 12x2 x f x x x 5x 14 3 2

12 Indiana Company began a construction project in 2024 with a contract price of 161 million to be received when the project is complete 2026 During 2024 Indiana incurred 35 million of costs and estimates an additional 84 million of costs to complete the project Indian recognizes revenue over time and for this project recognizes revenue over time according to the percentage of the project that has beer completed 01 26 29 Indiana Note Do not round intermediate calculations Present final answer in millions to 2 decimal places Multiple Choice recognized no gross profit or loss on the project in 2024 recognized 35 00 million loss on the project in 2024

her the following statement is true or false If r 0 1 there is a strong negative correlation between two variables Choose the correct answer below OA The statement is false because a value of r 0 1 means that there is no relationship between two variables B The statement is true because a value of r 0 1 means that there is a strong negative relationship between two variables C The statement is false because a value of r 0 1 means that there is a weak positive relationship between two variables A D The statement is false because a value of r 0 1 means that there is a weak negative relationship between two variables

f x Identify any x intercepts and y intercepts in the graph of the function Identify the coordinates of any holes in the graph of the function State the equations of any asymptotes in the graph of the function Answer 7 def x x 6x 2x3 8x p

Put the following equation in slope intercept form y 4 5g z x 8

Find an equation of the line that goes through the points 4 38 and 3 29 Write your answer in the form y mx b y

If Log 2 0 30103 Log 3 0 47712 and log 7 0 84510 then calculate 35 Log 28