Quadratic equations Questions and Answers

10 E 4 11 BOOKS NEVER WRITTEN Yours Forever by 84 20 5 3 11 5 8 The Incompetent Bullfighter by 8 3 3 2y 3 3 20 32 23 3 2 61 Niw X 1 6x 15 k 5 5 20 33 29 ABOVE ARE THE TITLES OF TWO BOOKS NEVER WRITTEN TO DECODE THE NAMES OF THEIR AUTHORS FOLLOW THESE DIRECTIONS Solve each equation below and find the solution in the code Each time the solution appears write the letter of that exercise above it 3 33 43 11 33 12 38 21 4 4 16 16 7 2 21 3 2 1 8 a 33368 12 11 12 84 20 7 5 3 N A M R 11 11 4 D L 818 9 7 10 d 5 d 2 X 2x 3 4 15 17 4x 12 11U u 14 15 21 y 8 3 15 4 15 8x 3 5 32 3 2n 3 5n 1 6 1 2 2x

Find the measure of angle b 11 13 15 244 65 b 39 Find the value of x 17 35 2x 16 4x 3 12 14 16 18 60 46 85 6x 2 56

3 Find the measure of each angle indicated 11 13 15 125 100 110 53 4 12 14 16 18 47 84 111 p 7 113

Let f x x 2 x 1 a Enter the domain of f g x in interval notation and g x infinity 2 U 2 infinity That s not it b Enter the domain of g f x in interval notation infinity 3 U 3 infinity That s not it Preview E 2 U 2 00 Preview E 3 U 3 00

Complete the proof that ASUV AUST S 1 2 3 U Statement SV TU STUV SU SU 4 ASUV AUST T Reason Given Given Reflexive Property of Congrum CPCTC Definition of coner ence

6 x 1 a Enter the domain of f g x in interval notation Let f x 5 x 2 and g x b Enter the domain of g f x in interval notation

Suppose h x For each function f x below find a function g x so that h x f g x a f x 3x g x b f x 4 X g x 6 x 12 c f x 45 6 x 5

The graph below shows the functions f x and g x 5 g x b f g 2 Y 5 5 f x 5 A X Use the values in the graph to compute the following compositions a f g 1 f g 1

The table below defines f x and g x for certain values of x b g 1 g 1 X 2 1 0 1 2 3 Use the values in the table to compute the following function compositions a f g 1 g 1 c a f 0 f x g x 17 15 2 2 3 22 2 3 1 2 1 0

2 Let f x x and g x x Find each of the following Enter DNE if not possible a fog 5 b gof 5 c fog 2

Let f x x 5 and g x 7x E Find each composition below a fog x

4x 4 and g x 4 and g x 3x Evaluate the following expressions and enter DNE if the expression is undefined a Evaluate f g 1 Let f x 4x b Evaluate g f 1

h x x 1 1 ifx 2 1 if x 2 Find h 5 h 2 and h 0

8 What are the factors of the polynomial function Use the rational root theorem to determine the factors f x x x 10x 8 The possible rational roots are 1 2 4 8 x 1 x 1 x 2 0 x 2 0 x 4 o x 4 o x 5

6 Is the binomial a factor of the polynomial function f x 2x 15x 22x 15 Select Yes or No for each binomial and explain x 3 x 3 x 5 2x 1 2x 1 Yes No

Graph the following function by hand and support your skelch with a calculator graph Give the domain range and the equation of the asymptote Determine iftis increasing or decreasing on its dom 100 10 Graph the function y 10 Choose the corect graph below OA OB Give the domain range and equation of the asymptote The domain is Type your answer in interval notation The range is Type your answer in interval notation The equation of the asymptote is S Oc

Find the exact value of the expression given below cos 75 C core O Points cos 75 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominato

Use identities to fill in the blank If tan 0 12 5 then cot 0 cot 0 Type an integer or decimal

1 Use the points on the number line to answer a c A C 3 7 36 49 a Which point best represents 47 b Which point best represents 272 c Which point best represents VTI B ot 4 5 D a 9 1 b 9 4 c 9 7 E 2 Estimate the value of 13 by plotting it on a number line Between and Decimal estimate 4 Miranda bought a square frame that has an area of 30 square inches What is the approximate side length of the frame to the nearest tenth 6 Which of the following is the best estimate of 90 6 P 4 Band A 9 16 E 5 25 7 6 36 8 3 Estimate the value of 150 by plotting it on a number line Between and Decimal estimate 5 Tristan wants to build a square garden in his backyard that will cover an area of 75 ft If Tristan has 32 feet of material for the perimeter of the garden does he have enough Explain 7 Which of the following statements is not true a The square root of 112 is between 10 11 b The square root of 180 is between 13 14 c The square root of 12 is between 4 5

3 Which graph represents f x 2x8 Explain how you know based on the sign of the leading coefficient and degree of function

7 Which statements are true about the polynomial function Explain why each statement is or is not true f x 3x 4x 13x 6 O O 0 O x 3 is a factor of f x O f x 0 when x 3 3x 2 is a factor of f x f 1 0 o f x divided by x 1 has a remainder of 0 f x 0 when x 3 3x 2 is a factor of f x

4 Explain the difference between 5 2 and 52

5 Divide x4 3x 55 x 3

9 One of the zeros of the polynomial function is 5 What is the factored form of the function f x x 4x 6x 4x 5 o x 5 x 5 x 1 x 1 o x 5 x 1 x 1 o x 5 x 1 x 1 x 1 x 1 x 5

10 What are the zeros of the polynomial f x x x 16x 4x 48

1 The table shows ordered pairs for a polynomial function f What is the degree of f 77 7 2 3 f x 82 17 2 17 82

For the function f use composition of functions to show that 5 7 1 x 7x 1 x 3x 7x 1 is as given 7 To show that f x x find f of x and 1 of x and check to see that each is x only f o f x is is x each is x at least one is x

3 2 1 0 1 2 3 f x 82 17 2 I 2 17 82 2 Which graph represents f x x Explain how you know based on the sign of the leading coefficient and degree of function

Determine whether the function is one to one If it is find a formula for its inverse f x 4x 9 Is the function one to one No Yes Find a formula for the inverse if it exists Select the correct choice below and fill in any answer boxes within your choice A x 0 Simplify your answer OB There is no inverse function

For the following function a determine whether it is one to one b if it is one to one find its inverse function f x x 6 Is the given function a one to one function Select the correct choice below and if necessary fill in the answer box to complete your choice O A Yes the function is one to one The inverse function is f x Simplify your answer B No the the function is not one to one

Daniel claims that if a graph of a quadratic function has zeros at 4 0 and 2 0 then the factored form of the quadratic function could be written as f x x 4 x 2 Is Daniel correct A Yes Daniel correctly wrote out a factored form of a quadratic function with zeros at 4 0 and 2 0 B No Daniel should have written the factored form as f x x 4 x 2 C No Daniel should have written the factored form as f x x 4 x 2 D No Daniel should have written the factored form as f x x 4 x 2

Let f x x 2 Graph a function g which represents a horizontal translation to the right 3 and a vertical stretch by a factor of 2 of the function f Ray Tool Directions 1 Be sure the Ray Tool is on it should be dark grey 2 Click once on the coordinate plane to place the endpoint of the ray 3 Click once on another point to create a ray that goes through your new point 4 Repeat to make another ray as necessary 5 Use the Undo Redo and Reset buttons as necessary to make changes RAY 10 9 A EDIT LABEL

11 How many complex zeros does the function have Explain f x x 3x 5x 3x 6 12 Factor the polynomial function f x x 2x 6x 4x 16

4 The amount of money Veronica has in her savings account after a months is shown in the scatterplot below Savings 3000 2500 2000 1500 1000 500 A 0 B 50 1 2450 2 2150 c 200 3 2100 4 1700 5 1600 6 1450 0 2 4 7 1300 6 Months 8 1000 9 750 8 10 600 10 12 Based on the trend shown in the scatterplot which of the following best represents the amount of money Veronica will have in her savings account at the end of 12 mon A DO

3 Which graph represents f x 2x Explain how you know based on the sign of the leading coefficient and degree of function 4 Use synthetic division to divide 4x 6x 23x 10 by x 2 5 Divide x4 3x 55 x 3

8 What are the factors of the polynomial function Use the rational root theorem factors f x x x 10x 8 The possible rational roots are 1 12 14 18 x 1 o x 1 x 2 x 2 x 4 o x 4 o x 5 O O 9 One of the zeros of the polynomial function is 5 What is the factored form of the function f x x 4x 6x 4x 5 o x 5 x 5 x 1 x 1 o x 5 x 1 x 1 o x 5 x 1 x 1 o x 1 x 1 x 5 10 What are the zeros of the polynomial f x x x 16x 4x 48

Werts a function g whose graph represents a translation 2 units down and 3 units to the right of the graph of f gla

The table below shows the amount of water that is in a fish tank being filled Minutes Gallons of Water 1 A f x 5x 12 B f x 5x 7 f x 7x 5 D f x 12x 5 12 2 17 3 22 4 27 Which of the following functions could model the amount of gallons of water f x that the fish tank will contain after a minutes of being filled

What are the domain restrictions of Oq 1 and q 8 O q 1 and q 8 Oq 1 and q 4 O q 1 and q 4 q 7q 8 q 3q 4

and supply CHIMEDELE System by Elimination Solve each system by elimination O 401 39 0 10y 19 3y 0 A 3 1 C 6 1 x 28 2 018 V Bi 3 1 Dj No solution 8 01 8 EZ 777 A 1 2 1 1 8 CH 10 2 D Infinite number of solutions 48 52 01 E r 1 137 1 V 291 Z Z 8 D 4 2

Simplify 2x 2 x 2x 1 O 2 O 1 x 1 O 2 x 1 2 2 1 1

Which expression is equal to O O O O x 4 x 2 x 2 x 4 x 2 x 4 x 2 x 4 x 2 x 4 x 4 x 4

Which expression is equal to O O O 75 7m 7m5 n4 n5 7m5 4mn8 28m5n 7

What are the domain restrictions of the expression Select each correct answer Oy 8 O y 5 O y 4 0 y 5 Oy 8 Oy 4 y 3y 40 y 9y 20

Which is the inverse of f x log 216 C 6216 A B 216 6 216 D X 216 x

8 A student is determining if two functions are inverses of one another The student completes the following computation and concludes that yes the functions are inverses Is the student correct f x 3x 5 g x 5 f g x 3 35 5 x g f x 3x 5 5 3 x A The student is correct because f x is found by adding 5 and multiplying by 3 B The student is correct because the function composition f g x x and the function composition g f x x C The student is incorrect because the functions are not opposites of each other D The student is incorrect because the function composition f g x x and the function composition g f x x proves nothing

5 Matthew claims that the function g x x 2 5 is the inverse of the function of f x 2x 5 Which statement provides a correct analysis of Matthew s claim A Matthew s claim is correct because if you add 5 to g x and then multiply it by 2 you get f x B Matthew s claim is correct because when g x is substituted into every occurrence of x in f x f g x x and when f x is substituted into every occurrence of x in g x g f x x C Matthew s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x 5 therefore g x is not the inverse of f x D Matthew s claim is incorrect because when g x is substituted into every occurrence of x in f x f g x x therefore g x is not the inverse of f x

1 3 ut a ftware System by Elimination Solve each system by elimination 1 0 6x 8 10y 10y 19 3x 0 A 3 1 C 6 1 3 1 3 y 1 x 4 x 28 2y A 8 10 C 8 10 5 x 15 9 y A 7 10 C 4 10 2 2 044 8x 36y 7 8x 4y 4 9 12y 3x A 8 1 C 1 1 B 3 1 D No solution 9 1 5x 2y 10y 8x 46 A 3 7 C 1 7 B 10 8 D 8 9 B No solution D 7 10 B 1 1 D 1 1 B 3 7 D 3 7 All rights reserved 2 2 x 5 4 4 4 9 x y 5 5 6 8 9 y 0 44 0 2x 8y 4 1 y x 0 2 10 A 1 2 B 1 1 C 10 2 D Infinite number of solutions A 2 2 C 6 2 6 20 9y 5x 6x24 18y 0 A 0 6 C 4 0 8 9y 7x18 6x 9 7y A 9 9 C 9 9 B 2 2 D 4 2 A 2 3 C 2 9 B 0 8 D 0 8 B No solution D 9 9 10 24 9x 2y 0 5y 29 7x B 9 2 D 2 9

1 7 ut a System by Elimination Solve each system by elimination 1 0 6x 8 10y 10y 19 3x 0 A 3 1 C 6 1 1 3 3 3 1 4 x 28 2y A 8 10 C 8 10 5 x A 7 10 C 4 10 15 9 2 2 0 44 8x 36y 7 8x 4y 4 9 12y 3x ftware LLC All rights reserved A 8 1 C 1 1 9 1 5x 2y 10y 8x 46 A 3 7 C 1 7 B 3 1 D No solution B 10 8 D 8 9 B No solution D 7 10 B 1 1 D 1 1 B 3 7 D 3 7 2 6 8 5 4 4 4 9 x y 5 5 A 1 2 B 1 1 10 9 y 0 2 x 44 0 2x 8y 4 1 1 y x 0 2 C 10 2 D Infinite number of solutions A 2 2 C 6 2 6 20 9y 5x 6x24 18y 0 A 0 6 C 4 0 8 9y 7x18 6x 9 7y A 9 9 C 9 9 B 2 2 D 4 2 A 2 3 C 2 9 B 0 8 D 0 8 B No solution D 9 9 10 24 9x 2y 0 5y 29 7x B 9 2 D 2 9

1 3 ut a ftware System by Elimination Solve each system by elimination 1 0 6x 8 10y 10y 19 3x 0 A 3 1 C 6 1 3 1 3 y 1 x 4 x 28 2y A 8 10 C 8 10 5 x 15 9 y A 7 10 C 4 10 2 2 044 8x 36y 7 8x 4y 4 9 12y 3x A 8 1 C 1 1 B 3 1 D No solution 9 1 5x 2y 10y 8x 46 A 3 7 C 1 7 B 10 8 D 8 9 B No solution D 7 10 B 1 1 D 1 1 B 3 7 D 3 7 All rights reserved 2 2 x 5 4 4 4 9 x y 5 5 6 8 9 y 0 44 0 2x 8y 4 1 y x 0 2 10 A 1 2 B 1 1 C 10 2 D Infinite number of solutions A 2 2 C 6 2 6 20 9y 5x 6x24 18y 0 A 0 6 C 4 0 8 9y 7x18 6x 9 7y A 9 9 C 9 9 B 2 2 D 4 2 A 2 3 C 2 9 B 0 8 D 0 8 B No solution D 9 9 10 24 9x 2y 0 5y 29 7x B 9 2 D 2 9