Quadratic equations Questions and Answers

Use the figure to determine the radian measure of angle 8 0 radians C CLB

2 Factor 81x8 36y 2 3 Factor 5x 23x 12 4 Factor 125x6 27y15

6 What are the roots of the equation x 4x 5 7x 13 0 7 What are the roots of the equation 3x315x 18x 0

x 12x 34 9 Solve x 7x 3 0 10 What is the solution of the equation over the complex numbers x 12 0 11 Solve for x over the complex numbers x 6x 25 0

12 What is the factored form of the expression over the complex numbers 25x 16y

Find the radius of the circle in the figure to the right The radius of the circle is Type an integer or a simplified fraction CE 27

elect the correct answer from each drop down menu omplete the statements about the graph of a function When a graph is symmetric about the origin it is an When a graph is symmetric about the y axis it is an function is considered function function if f x f x and it is considered if f x f x

If f x 5x In 6x then f x f x f x f 5 x ZISNA

Write the slope intercept form of the equation of the line through the given points 5 through 0 3 and 5 5 6 through 0 4 and 2 0 4 A y x 3 A y 2x 4 C y 4x 2 4 B y 3x 5 8 C y x 3 8 D y x 3 7 through 2 2 and 1 3 A y x 8 C y 8x 1 B y 5x 1 D y 5x 8 9 Slope 2 y intercept 1 A y x 2 C y 2x 2 11 Slope 2 A y 2x 2 C y 2x 2 B y 2x 1 D y 2x 2 y intercept 2 6 Write the slope intercept form of the equation of each line given the slope and y intercept 10 B y x 2 D y 2x 2 8 12 8 through 1 4 and 0 4 A y 4 C y 4x 12 Slope 10 Slope 4 y intercept 5 A y 3x 4 C y 4x 5 4 3 4 A y x 3 B y 4x 2 D y 2x 4 C y x 4 B y 2x D y 4x 3 B y 3x 4 D y 5x 4 y intercept 1 4 B y x 1 4 D y x 1 3

f x x 3x and g x 1 6 a f g x Domain of f g x b f g x Domain of f g x c fg x d Domain of fg x Domain of

7 Write the slope intercept form of the equation of the line through the given point with the give slope 8 7 through 4 5 slope 1 12 A y x 3 C y x 3 9 4x 7y 7 4 A y x 1 4 C y x 1 B y x 3 2 D y 3x 3 11 x y 1 A y 3x 1 C y x 3 5 B y x 1 7 Write the slope intercept form of the equation of each line D y x 4 B y x 1 D y x 1 7 8 through 1 3 slope A y x 12 B y x 4 4 11 1 D y C y 4 11 1 4 X 10 10 3x 5y 30 A y 6x 3 5 4 11 1 4 3 B y 6x 5 4 3 C y x 6 5 3 D y x 6 12 2x y 4 A y 4x 2 C y 4x 2 1 4 B y 2x 4 D y 2x 4

Q2 6 points Calculate V12 numerically by using Newton Raphson and Secant methods Use initial guesses of 3 and 4 for the Secant while initial guess of 1 for Newton Raphson method Calculate until the percentage of relative approximate error becomes less than 1 Hint This can be solved by finding the root of f x x 12 Round off all your calculations to four decimal places when it is required

317 Implus 3 1 Newton I 1 22 t S N S I Ft 34120251 HIST2 N S F m 2 2 T m L ML7

Given F 0 cos x 0 C y 2 4 y 0 z 0 0 x T which of the following is a normal vector of cylinder C O 0 cos u 0 O None of the statements are normal to the cylinder O 2 cos u u 2 sin u O 0 2 cos u 2 sin u fa 2 coc 2 sin 2ul

Identify the value of n in the diagram n 8 3n 7 On 4 5 O n 9 O n 8 n 10

The graph of a 4th degree polynomial f x is shown below 15 f x 10 5 4 0 0 0 4 0 5 2 1 5 10 C 5 Find the rule of this function Enter your answer in either factored or expanded for

The graph of a 4th degree polynomial f x is shown below 30 3 294 20 872 20 20 3 794 6 623 0 2 1 0 5 0 5 0 10 10 Find the rule of this function Enter your answer in either factored or expanded for

9 Use the converse of the Pythagorean theorem to show that the vertices 2 1 4 0 and 5 7 form a right triangle Compute the area of the triangle

Find the values of x sa t

5 Find the equation of the line through 2 3 with a slope of 0

Compute the distance between 2 4 and 4 10

3 Find the equation of the line through 1 1 and parallel to y 2x 4

The graph of a 4th degree polynomial f x is shown below LO f x 5 0 LO 0 1 2 5 0 0 4 0 5 Find the rule of this function Enter your answer in either factored or expanded form

f x 10x55x4 8x 3x 5x 8 Without graphing the function answer each of the following questions a Identify the degree of f b Identify the leading coefficient of f c Identify the y intercept of f Write your answer as an ordered pair d Describe the end behavior of f As x f x As x o f x O O As x f x As x o f x As x f x As f x

Find the equation of the line passing through 2 3 with undefined slope

a Enter the general expanded form of g x g x Roots on has factored form g x x x 1 x b Identify the roots of g x Separate multiple answers with a comma If a root has multiplicity m enter it m times c Identify the degree of g x degree d Identify the leading coefficient of g x leading coefficient e Describe the end behavior of g x O As x g x o and as a g x O Asx g x and as o g x 3

O O O O 7 6 5 7 f x x 2 x 5 f x x 2 x 5 f x x 2 x 5 f x x 2 x 5 3 V 5 5 4 S 3 6 2 1 2 4 3 5 6 7 2 A 6

20 6 17 O f x x 2 x 5 O f x x 2 x 5 O f x x 2 x 5 O f x x 2 x 5 to to 5 6 5 t 3 2 1 4 2 3 7 5 6 7 4 5

6 O 5 co O f x x 2 x 4 x 5 O f x x 2 x 4 x 5 O f x x 2 x 4 x 5 f x x 2 x 4 x 5 7 6 5 3 2 1 1 2 3 4 5 6 7 2 3 4 5 6

Using the graph of the function y f x answer the following questions Y Interval s 5 Interval s 5 A to 5 4 3 2 2 Shift Mouse Wheel to zoom Shift Mouse Drag to pan a On what intervals is f increasing Enter your answer in interval notation X 8 b On what intervals is f decreasing Enter your answer in interval notation

Find the exact function value 3x 4 cot 3 cot Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Which one of the following vectors is a normal vector for any line which is parallel to the line 5x 4y 2 OA 5 4 OB 4 5 OC 2 3 O D 4 5 O E 3 2

nvert the radian measure to degrees Points 2 radian s Round to the nearest r

The function f is given by f x x 3 When f is rewritten in the form f x x ax bx cx d which of the following values is greatest

Convert the following radian measure to degree measure 1 R 4

Convert the following radian measure to degree measure 7T 4

Convert the following radian measure to degree measure T 2

onvert the following degree measure to radians 0 Points 0 of 1 330 radian s Simplify your answer Use integers or fractions for an exact answer using as needed

Convert the following degree measure to radian measure 90 Question 5 3 1 11 HW Score 0 0 of 28 points Points 0 of 1 90 radians Simplify your answer Type an integer or a fraction

Find the product 7 2i 3 6i 7 2i 3 6i Simplify your answer Type your answer in the form

Determine whether the given set of ordered pairs a 6 1 b 6 5 and c 0 2 are the solutions of the system of equations 5x 10y 20 2x 4y 8 a Is 6 1 a solution of the system Choose the correct answer below OA No because it satisfies both the equations OB Yes because it satisfies both the equations OC Yes because it satisfies the first equation O D No because it does not satisfy at least one equation b is 6 5 a solution of the system Choose the correct answer below OA Yes because it satisfies both the equations OB No because it satisfies both the equations OC Yes because it satisfies the first equation OD No because it does not satisfy at least one equation a ln 0 a solution of the system Choose the correct answer below

Solve the following system by graphing y 4x 3 12x 3y 9 Use the graphing tool to graph the system Click to enlarge graph Solve the system Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution is Type an ordered pair OB There are infinitely many solutions C There is no solution CALL 10 B o 8 6 4 2 2 6 8 10

A pole that is 3 5 m tall casts a shadow that is 1 52 m long At the same time a nearby tower casts a shadow that is 45 5 m long How tall is the tower Round your answer to the nearest meter m X 5

9 7 11 C y x 3 D y 7 through 2 2 and 1 3 A y x 8 C y 8x 1 B y 5x 1 D y 5x 8 Write the slope intercept form of the equation of 10 9 Slope 2 y intercept 1 A y x 2 C y 2x 2 11 Slope 2 A y 2x 2 C y 2x 2 B y 2x 1 D y 2x 2 y intercept 2 B y x 2 8 D y 2x 2 12

Describe any 3 out of the 4 features listed below for the function g x log x 4 1 Include a description of how you found those answers using complete sentences 1 Vertical Asymptote Name the equation of the asymptote and tell me how you found it from the equation or where you found it on the graph 2 X and Y Intercepts Name the x and y intercepts and tell me how you found them from the equation or where you found them on the graph 3 Transformations compared to its parent function f x log2 x You can just list the specific transformations that occurred such as vertical shifts horizontal shifts stretch or compress any reflections 4 Domain Name the domain of this function and tell me how you found it from the equation or where you found it on the graph

2 A school holds a lunch fundraiser The school has 350 students 70 of the students order lunch 15 of the students who order lunch select sandwiches The rest of the students who order lunch select pizza Determine the number of students who order lunch and select pizza Show your work

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