Quadratic equations Questions and Answers

Review What would be the next step in solving the following equation for x 2x 3 6 Divide both sides of the equation by 2 Multiply both sides of the equation by 2 Add 3 to both sides of the equation Subtract 3 from both sides of the equation

1 X 2 10 4 3 2 4x 10 Independent Practice 2 2x3 5 4 4 x 5 11

Which function is modeled in the table f x 1000 800 640 512 X 1 2 3 4 f x 1000 0 80x 1000 0 20x 1000 0 80 X 1 1000 0 20 X 1 O

If log 3 19 and log 2 12 then evaluate the following expression In 9 In 16 In b In b 07 037 0 10 086 05

1 Solve for x and simplify the answer a 6x 2x 3 0 b

8 When you fold a piece of paper in half once you have 2 regions If you fold a paper in half twice you have 4 regions a Explain in words what happens to the number of regions each time you fold the paper in half b How many times do you have to fold a piece of paper in half to get 64 regions c Write an equation for r the number of regions if you fold a paper in half k times d Write an equation for k the number of times you must fold a paper in half to get r regions e Which of your two equations could you use to figure out the answer in part b

discuter en fonction des param tres ventuels 2x b y z x 2a y z x 6a b y 6a b z

Solve the system by substitution 4x 7y 3 9y 27 2x O A OB O C O D 57 81 3 3 25 25 81 25 81 25 33 50 297 50 81 57 25 25 25

1 9 16 x y 36 OA G OB quantes Q G O C O D

9 x2 6 X 2 OA 7 2 2 OB O C 4 3 2 IN 2 2 OD 2

Give the domain and range of the relation 3 8 2 8 7 5 5 0 OA The domain is 7 2 3 5 The range is 8 5 0 8 OB The domain is 8 7 5 2 The range is 3 5 8 OC The domain is 3 5 8 The range is 8 7 5 2 OD The domain is 8 5 0 8 The range is 7 2 3 57

Which is the only relationship below that could NOT be modeled by a linear function Hours Worked Pay Hours Worked Pay 3 36 Hours Worked Pay 5 50 Hours Worked 0 Pay 450 1 20 4 48 6 60 1 450 2 30 5 60 7 72 3 450 3 40 6 72 8 86 12 450 4 50 8 96 9 102 30 450 5 60 www

A company wants to know how much to sell there hotdogs for at a minor league baseball game They have determined the price of the hotdog determines reasonably well how many hot dogs they will sell The following formula describes the number sold N based on the price p N 4p 20p 7 How may hot dogs will they sell at most if the formula is accurate 20 hot dogs 27 hot dogs 32 hot dogs 48 hot dogs HO

Graph the following polynomial function f x x 5x 300x Which of the following graphs correctly matches the graph of f x OA OB 10000 5 511 10000 150 O C 10000 O D 10000 10000 150

Solve the equation ex 6 O A 10 OB 4 O C O D X 6 18 5 12 5

Find a polynomial of degree 3 with only real coefficients and zeros of 6 4 and 0 for which f 2 1 Choose the correct polynomial of degree 3 with only real coefficients and zeros of 6 4 and 0 for which f 2 1 1 OA f x x 11 4 11 x 2 11 1 24 1 OB f x 1x3 48 1 1 1 O c f x x x 3x 48 24 x 2 1 O D f x x 4x 2x3 11 11

Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first 4x 3x 23x 16x 12 x 3 Is x 3 a factor of 4x4 3x 23x 16x 12 OYes O No

Determine if the function is even odd or neither f x 0 75x x 2 O Odd O Even

For the given functions f and g find gof x f x 4x 5x 8 g x 5x 4 OA 20x2 25x 36 OB 20x2 25x 44 OC 4x2 25x 36 OD 4x2 5x 4

5 6 pts Find all solutions in terms of integer k with initial solutions in the interval Show your work Give your answers in radians rounded to 2 decimals 15sin x 3csc x

3 5 3 5 7 A 6b 56 81b C 5 k 6 C k 5 C A C A A 2v 5 35v 45 k 7 2 k 2 7k 5 5 7k 2 k 8 k 2 B n 3 49n 14 3 B b D 5 n 6 n 7 n 1 6 n 2 D 14v 18v 4 36 B D k 1 4k k 7 k 8 v 2 v 9 100 9v 21n 64n 20 9n 30n B D n 3 21n 8

Product 56 35 32 24 42 6 14 1 6 121 32 25 40 52 6 1 54 16 Sum 1 12 3 5 1 5 9 2 5 0 14 24 6 9 5 2 15 10 Factors

Find two factors wh Sum 1 13 6 0 8 9 7 18 1 56 14 25 0 8 4 3 10 Product 6 36 16 4 33 20 6 81 12 55 48 100 49 7 3 28 21 Factors

2 9 00 9v 4n 20 30n B D n 3 21n 8 9n 6 8 6 3x 9 7 x 4 5x A C 10 30x 90 4 x 9 8 7n 6 18n 27n n 3 A 10n C n 9 n 2 B 1 D x 8 3x 2n n 6 21n 18 2 B 3n n 6 n 2 27n D

5 7 5 7 5 35v 45 A 2v C v 3 4 n 3 14v 18v B D v 2 v 9 100 9v 21n 64n 20

https goformative com formatives 65688b2942b8873217618387 7 9 7 9 A 2v C A n 3 49n 14 C v 3 4 A C n 1 6 n 2 D 5 n 6 n 7 3a 7 21a 64a 35 3 a 1 5a a 6 a 10 6 B 21n 64n 20 9n 30n V 2 v 9 100 9v B D asics Multiply Rati x B 14a 10a 5a 45 D n 3 21n 8 9n 2a 5 a 9 a 6 9a 20 23 Kuta Software LLC All rights 8 8 10 10 A A A C C 7n 18n C n X n 10 12k 5k 4 k k 3 6k k 3

Calculate the binomial coefficient 80 2

WHIR Togels The problems on this worksheet come from your book p 146 148 2 6 12 and 14 1 Driving Use your graphing calculator to make a scatter plot for this data set using gallons as the independent variable Identify the correlation and find the equation of the line of best fit Gallons Distance mi 11 2 338 Distance Traveled Mean Temperature F Heating Bill 9 8 296 10 6 332 10 1 324 Claire s Heating Bills 38 42 44 93 79 75 12 3 368 2 Home Economics Use the data relating the average temperature in a month to the heating bill at Claire s house that month 36 83 8 7 263 10 1 305 42 49 38 74 67 86 a Make a scatter plot using mean temperature as the independent variable b Find the correlation coefficient and the equation of the line of best fit Draw the line of best fit on your scatter plot c Predict the heating bill for a month in which the average temperature is 40 F How accurate do you think your prediction is 3 School Here are the number of teachers and the number of students at a randomly selected sample of high schools in a city Teachers and Students at Selected Schools Teachers 92 52 114 49 110 62 76 84 Students 1050 653 753 381 1312 813 496 910 a Make a scatter plot of the data using teachers as the independent variable b Find the correlation coefficient and the equation of the line of best fit Draw the line of best fit on your scatter plot c Predict the number of teachers in a high school that has 600 students How accurate do you think your prediction is

Divide State any restrictions on the domain x 12x 32 x 16 x 12x 32 x 16 x 8 x 2 x2 6x 8 9 x 8 x 2 x 6x 8 11

Let f x 6x 1 and g x Find f g x f g x fg x and 1 f g x 6x 1 Simplify your answer X f g x 6x 1 X Simplify your answer fg x 6x 1 Simplify your answer 7 x x x x 6x 1 Simplify your answer The domain of f g is Type your answer in interval ndation x Give the domain of each

1 a Question 1 7 NEXT BOOKMARK Keith received money from his family and friends for his birthday He decides to put the money in the bank Keith invests 3 050 at 13 7 interest compounded continuously Write an equation in y form to represent Keith s investment Use t for time 3 points 3 points x b If Keith s investment increases at the same interest rate each year how long will it take Keith s investment to double SHOW ALL WORK FOR HOW YOU SET UP THE PROBLEM AND USE LOGARITHMIC PROPERTIES TO ALGEBRAICALLY SOLVE THE PROBLEM

36 100 1 What are the foci of the ellipse 10 10 Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed What is the domain Type your answer in interval notation Round to the nearest integer as needed Use a comma to separate answers as needed What is the range porost integer as needed Use a comma to separate answers as needed

X 3 1 0 4 g x 5 1 1 9 h x x x 4 O 5 O 3 O 3 O 5

OR Reduce the quadratic form 3x 2y 3z 2xy 2yz to normal Under form and discuss the nature of quadratic form

2 0 5 Write a possible polynomial function for the graph given above 4

ich of the polynomial functions in the list might have the given graph Circle all that apply a y x 1 x 2 b y x 1 x 2 c y x 1 1 4 2 d y x 1 x 2 e y x 2 x 1 2 x f y x 1 x 2 x 1 1 2

Sketch each of the following polynomial equations 3 f x x x 4 x 3 4 g x 3x 1 x 2

Use rational exponents to simplify each radical Assume all variables are positive x x

Simplify the expression Assume all variables are positive 4 7 x y N 1 3 4 64x y w 3

Consider the function y 12 sec x 7 What the amplitude of the corresponding cosine function Sketch the function T

Multiply and simplify the rational expression x 25 x 3x 40 2 2 X 64 x 2x 35 x 25 x 3x 40 x 64 x 2x 35 Simplify your answer Type your answer in factored form

Find the graph of the following ellipse Identify the domain range center vertices x y 25 16 A 1 AY What are endpoints of the minor axes of the ellipse 0 4 0 4 Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed Which graph is correct What are the foci of the ellipse hts of the minor axis OB www Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed OD O

a Find the intercepts of the graph of the following equation b Graph the equation 5x 8y 20 Il necessary I answer box to complete your choice O A The x intercept is Type an integer or a simplified fraction B There is no x intercept What is the y intercept Select the correct choice below and if necessary fill in the answer box to complete your choice O A The y intercept is 3 5 4 34 12 1 3 My 4

Solve the following equations for the unknown variable value clearly showing your work to both sides of the equation 2 8 4x 4 x 12 8 1 21 12 4 10 3 1 2 x 8 X 6 8 1 0 10 2 X 12 L 4 8 32 10 S 5 So X 9 2 x 10 d l X 8

Write an equation of the line Express the answer using either the general form or the slope intercept form of the equation of a line Q The equation of the line is Type an equation Use integers or fractions for any numbers in the expression

Graph the line that contains the point P 5 5 and has an undefined slope Find an equation of the line Use the graphing tool to graph the line Use the given point to graph the line Click to enlarge graph Write the equation of the line that contains the point P 5 5 and has undefined slope 10 10 8 6 4 2 di 2 4 6 84 ts 10

Solve the linear inequality Express the solution set using set builder and interval notation Graph the solution set 2 3 5x 24 4x The solution set expressed in set builder notation is x The solution set expressed in interval notation is Choose the correct graph of the inequality below O A 15 0 15 O B 15 0 15

Solve the inequality Write the solution in interval notation and graph it 6x 1 19 OA 3 00 OC 0 3 Choose the correct graph of the solution O A O B C OP OB 3 00 OD 0 3 1

What is the equation of the following parabola in vertex form 5 4 3 2 1 31 2 11 21 31 4 2 3 4 5 y 5 x 2 4 y 5 x 2 4 y 5 x 2 4 y 5 x 4 2

Which of the below is the factored form of the polynomial showr m 6m 40 n 8 n 5 n 10 n 4 n 10 n 4 n 12 n 6